“Sweet and sour?” Patti LuPone suggested, as if considering options on a menu. She looked questioningly at Mia Farrow, who was sitting next to her in a small atelier in a Midtown Manhattan hotel. We were in the heat-soaked throes of early August, and the women had just arrived, depleted, from what they described as an “airless” rehearsal room nearby.

“I don’t know,” LuPone said. “It’s kind of negative, the sour …” She hesitated. “SALTY!,” she then exclaimed, in the clarion voice that has resonated from so many stages over the past five decades. “Sweet and salty.”

LuPone was trying to define the yin and yang of the most unexpected double act of the new Broadway season. Farrow (she would be the sweet) and LuPone (salty) are the stars and entire cast of Jen Silverman’s “The Roommate,” which is in previews and opens on Sept. 12 at the Booth Theater, under the direction of Jack O’Brien.

They portray women of radically dissimilar backgrounds and temperaments, who come into intimate and potentially combustible contact. These are roles for which Farrow and LuPone, longtime friends who have homes in the same Connecticut county, would seem to be naturals. “We complement each other, because we are so different,” LuPone said.

Farrow, whose habitual manner melds openness with wariness, said: “I don’t know if at the core we’re so different. We may superficially appear to exhibit certain things that are ours in different ways. But going deeper than that. …” Her voice trailed into an ellipsis.

Within that ellipsis, you have the essence of both Silverman’s play and the tantalizing pairing of its performers. A story of what happens when a meek Iowan homebody (Farrow) takes in a disruptive stranger from the Bronx (LuPone, natch) as a lodger, “The Roommate” ponders the Gordian knot of identity for two women at the crossroads of late middle age and the questions, as Silverman puts it, “of who gets seen and who doesn’t.”

“People find specific words for themselves because it’s easier than not having words,” LuPone’s character says in the play, which is Silverman’s Broadway debut. “But it doesn’t mean that those words are accurate all the time.”

When I first met LuPone and Farrow during the second of their three weeks of rehearsal, LuPone said, “Whatever anybody thinks about me is untrue. Period. Right?”

Farrow answered, “It’s probably pretty safe to say that.” Beat. “Unless it’s me.”

Audiences for “The Roommate” will no doubt be bringing their own preconceptions to the show. The production is a dramatic return to the Broadway stage for both stars. True, LuPone was there only a few years ago, in a Tony-winning run in a revival of Stephen Sondheim’s “Company.”

But not long after, she announced on Twitter that she had resigned from the labor union Actors’ Equity. “Gave up my Equity card; no longer part of that circus,” she wrote. “Figure it out.” (She has not renewed her membership, and said she is able to work on Broadway because of the Supreme Court’s “financial core” ruling, which makes it possible for a dues-paying nonunion member to work a union job.)

As for Farrow, though she appeared memorably in staged readings of “Who’s Afraid of Virginia Woolf?” (in 2000) and “Love Letters” (2014), she hadn’t been in a full-dress Broadway production since 1979, when she starred with Anthony Perkins in “Romantic Comedy.”

In recent years, she has been most visible for her participation in the 2021 HBO docuseries “Allen v. Farrow,” which focused on the allegations that the filmmaker Woody Allen, her personal and professional partner of 12 years, had molested their adopted daughter, Dylan, as a child. Allen has long denied the allegations.

The Connecticut house where Farrow now lives is smaller than the one in which she raised her 14 children. “I’m really happy just being home,” she said. In bluejeans, a sweatshirt and oval wire-framed glasses, with her fleece of pale, Alice-in-Wonderland hair worn down, Farrow still has what the critic Pauline Kael described as a “pale-pink eerie sprite face.” And at 79, she still emanates that uncanny feeling of translucence that turned her into a sui generis movie star in “Rosemary’s Baby,” Roman Polanski’s 1968 horror classic.

“I think she’s definitely a unicorn,” said Chris Harper, the British producer behind “The Roommate.” “There’s just a magic to her that means you can’t take your eyes off her.”

After he bought the rights to “The Roommate,” which had a 2017 run at the Williamstown Theater Festival, he sent the script to O’Brien, who has his own house in Connecticut. “Jack said early on, ‘I think this could be Mia Farrow’s play,’” Harper recalled.

“I thought, you know there really is nobody like that,” O’Brien said of Farrow, adding that he thought it was “too bad that at this point she’s in a sort of footnote to a sour” relationship.

LuPone agreed almost instantly to “The Roommate” when she learned Farrow was involved. (LuPone said that Annette Bening was their first choice for her part, but Harper and O’Brien said that isn’t true.) The first table read took place in late April in O’Brien’s living room.

O’Brien thinks of his stars in orchestral terms: LuPone is brass; Farrow, woodwind. Of the 75-year-old LuPone, and her gift for creating “seismic shocks” in performance, he said: “She’s Sicilian. She’s got things coursing through her body that normal people don’t have to deal with.” (LuPone: “I have pepper blood.”) O’Brien said he thinks of Farrow “as sort of a white witch.”

“She’s unique,” O’Brien said. “They both are. Put me in that rehearsal room, and I’m in bliss.”

Bliss was not perhaps the word for what Farrow was experiencing in early August. Staying in rented city digs, she said she had become “almost agoraphobic.”

Was she excited to be returning to theater? “I’ll be excited eventually,” she said evenly. “It’s not boring. I want to get it right. I’ve got to not disappoint Patti.”

“Aww, Miii-aaa,” LuPone wailed, stretching the name into long, plangent syllables. “You don’t disappoint me any time.”

In conversation, each woman can seem astonished by the other’s singularity. The expletive-prone LuPone speaks in capital letters; Farrow in droll, lowercase italics. (Asked about a streaming series she appeared in, Farrow answered, deadpan, “You know, a girl’s gotta earn a living, right?”)

LuPONE AND FARROW MET in the mid-1990s through the Broadway musical titan Stephen Sondheim, another Connecticut resident, whom both describe as an essential mentor. LuPone, who has appeared frequently in Sondheim revivals and concerts and spoken of the pains and pleasures of his criticism, has said that her first thought when she learned he had died in 2021 was: “Who will make me better?”

Farrow “never made a professional decision without checking with Steve,” she said. When Edward Albee, after seeing Farrow in “Virginia Woolf,” proposed she do his famously abstruse “Tiny Alice,” she called Sondheim, who told her, “‘Absolutely not.’”

“Well, I had an interesting experience with Edward Albee,” LuPone said. “Liz McCann” — the producer — “was after me, for Martha, in ‘Who’s Afraid of Virginia Woolf?’ So all of a sudden he decided I was too completely on the nose for it. Go figure that out.”

“And now he’s completely dead,” Farrow said sweetly. “So you can do it.”

“Now he’s completely dead,” LuPone echoed. “How can an actor be too on the nose for a role? I thought, ‘What the [expletive].’ Whatever.”

“My problem is I don’t know what to do when I don’t do this,” LuPone said. “I don’t knit!”

She tried gardening during the pandemic, she said, and “became obsessed with weeds, so much so that I kept spraining my thumbs, ripping them out.” She is not, she said, “self-motivated” and needs the schedule of the stage.

“Patti, your gift is enormous,” said Farrow, who grew up in Hollywood as the daughter of the director John Farrow and the movie star Maureen O’Sullivan (best known as Jane to Johnny Weissmuller’s Tarzan in the 1930s). “I can’t even imagine, but if we are to believe in God or a higher order, as Vaclav Havel would say, then that itself would drive you to express it. I don’t mean to get grandiose with you. But I don’t have that.

“If I did, I’m sure I’d feel differently. I’ve been married to André [the composer and conductor André Previn] and Frank Sinatra. They had to do what they did, because it was something they needed to express.”

LuPone and Farrow began acting at roughly the same age, 17 or 18 — LuPone as a student in the first drama division class at the Juilliard School in Manhattan, Farrow playing Cecily in an Off Broadway production of “The Importance of Being Earnest.” She had no professional experience or training, but her family needed money, and she said acting “didn’t seem impossible.”

LuPone has often said that she “cut my teeth” on the plays of David Mamet, in which she appeared before and after her star-anointing 1979 performance in the Broadway production of Andrew Lloyd Webber’s “Evita.” Though Mamet’s political views land far to the right of LuPone’s, she said they stay in touch.

“I think any kind of relationship where you learn,” she said, “where you’re answering to the thing you chose to do, you kind of excuse the abuse of some people, and the politics of somebody else. Because they are important in your development as a person and as a craftsman.”

I asked Farrow if anyone had played that role in her life. “An abuser?” she said, with raised voice and widened eyes. She went on to say, “There wasn’t one person ever.”

She has become a familiar presence on social media, posting her Wordle scores and spontaneous reactions to world events. LuPone has mostly retreated from such platforms, from which she once provided instant-legend, antic tours of her basement during the pandemic.

“There’s no mystery left in our stars,” LuPone said. “And everybody has permission to take issue. And it’s never kind. Why? Why are we exposing ourselves when our job is just to play a character?”

Farrow picked up the cue: “As we speak to a person who is interviewing us for our thoughts on all these things. How crazy is this? We’re contributing to a problem that we cannot solve, ever.”

A week later, they were dutifully perpetuating the problem by appearing on “Late Night With Seth Meyers.” I met them in the show’s green room, where LuPone was wearing a jaunty Thom Browne seersucker suit, while Farrow looked pristine in jeans.

We adjourned to a restaurant downstairs. LuPone ordered the beef carpaccio; Farrow asked, “Do you have anything in chocolate?”

Covering a collective century of lives in the public eye, their conversation acquired dizzying breadth. They recalled the party where they met, at LuPone’s house, when she had just returned from London after being fired from “Sunset Boulevard,” with a hefty settlement. (“You were saying ‘dirty money, dirty money,’” Farrow murmured gleefully.)

They discovered that they had both appeared as Irina, in Chekhov’s “Three Sisters,” in 1973, LuPone on Broadway, Farrow in London. “Oh my God!” said Farrow, who then mewled, “Oh, Moscow, Moscow!”

Perhaps more than any contemporary star, LuPone would appear to be Broadway’s ultimate avatar. But she is also one of its most conspicuous critics, and she discoursed vehemently on the timidity of commercial theater and the failings of Actors’ Equity. She explained why she is not a diva (a word that connotes bad behavior and “should be strictly reserved for opera singers”).

Farrow talked about being served divorce papers by Sinatra’s lawyer on the set of “Rosemary’s Baby,” when, at 22, she had thought: “He’ll never divorce me. I’m the love of his life”; LuPone, about crying herself to sleep over roles she didn’t get. Both women said they have many regrets. “Only a sociopath would have no regrets,” Farrow said. “That song, ‘Non, je ne regrette rien’? Impossible!”

And finally, both talked about those transporting, elusive moments onstage when everything coalesces into harmony, and it feels, Farrow said, like “a visitation from the gods.”

LuPone spoke about how often that happened when she was playing Mama Rose in the 2008 revival of “Gypsy,” directed by a 91-year-old Arthur Laurents, its imperious and inspiring librettist. Farrow remembered the nights when such rare moments occurred during “Romantic Comedy” and wondering at the time if she could ever consciously recreate that point “where there’s just no sense of self.”

Now she has the chance to experience that kind of transcendence again. Farrow said she has gotten past the early period of wondering “What was I thinking?” and feeling homesick. “We’re at a point in rehearsal where it’s actually getting fun,” she said. “So I’m thinking I’m opening a door that I may never open again. …”

“And it would be our loss if you don’t open the door again,” LuPone said, leaning urgently toward Farrow. “Because you’re so great. There’s something so magical about you, Mia!” she said, using a Mametian adverb to modify “magical.”

Farrow looked startled by the description. “I never believed in myself,” she said. The eyes of both women shone with tears, as they glowed across the table at each other in the artificial twilight of the restaurant.