For someone who commands such large, ambitious productions, Elliott is strikingly inward, even openly insecure. “I’m not the best choice for this play,” she told me when we first met, over lunch at the Jane Hotel. “I’m female, I’m English, I’m not in any way Mormon or Jewish. I wasn’t affected by AIDS directly. So there are lots of reasons why I shouldn’t be doing it. But I feel like it is my story.” “Angels,” she went on, depicts people “stripping off their identities and redefining themselves.”

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When I asked how that was her story, she laughed. “Well, on a general level, I have a crisis of confidence,” she said. “I don’t often think that I can do it. And yet here I am. I hate public speaking. When I was a kid, I never spoke. I would sit under a table and not speak to anybody. No words for years. So to be in a position now where I’m leading a huge company of people and having to stir them and infuse them and inspire them every day, that’s not an easy thing.”

Yet beneath her timidity is tenacity. The producer Chris Harper, with whom she recently formed the company Elliott & Harper Productions, told me, “She becomes a kind of warrior. She’s, like, ‘I am not going to let go. I know how to do this.’ There’s total fearless absolute insistence. She’ll take on anybody.”

In 2016, “anybody” was Stephen Sondheim. Elliott wanted to direct “Company,” his 1970 musical about a thirty-five-year-old man named Bobby, who is struggling with romantic commitment. Elliott, finding the play’s concerns dated, wanted to make Bobby a woman. “I looked around, and I was surrounded by thirty-five-year-old women who are in my profession and thinking they should settle down,” she explained. “And, if they do, they should do it quickly, because of the biological clock. But what does that mean in terms of their career?”

Sondheim had recently rejected the notion of an all-male “Company,” which the director John Tiffany (“Once”) had proposed. Elliott met with Sondheim at his New York town house and pitched her gender-swap concept. He agreed to let her workshop the idea and asked her to send him a tape. She returned to London and did just that. “I asked him to have a few people sitting with him when he watched it—some younger people, some women as well,” she said. Harper told me, “She would have wrestled him to the ground.” But she didn’t have to. Sondheim gave her his blessing, and “Company,” with the main character renamed Bobbie, will open in the West End this fall.

Directors of “Angels in America” have employed various levels of spectacle. George C. Wolfe’s original Broadway production used lavish effects, as did Mike Nichols’s HBO film. But the Belgian director Ivo van Hove set his production on a bare stage, and the Angel was a male nurse in hospital scrubs. Before rehearsals for the latest version began, Elliott and her set designer, Ian MacNeil, spent a year and a half hashing out the design, meeting every few weeks at MacNeil’s apartment, in Shoreditch. They read each scene aloud, Elliott recalled, “trying to park the paranoia of ‘How the fuck are we going to do this?’ ” MacNeil, who is gay, and lived in New York in the eighties, gave Elliott a crash course in gay culture, playing her Shirley Bassey and Kraftwerk and Cole Porter and Wagner. “We listened to Judy Garland a lot,” Elliott said.

They had two big breakthroughs. The first was deciding on the look of the Angel. Elliott envisioned her not as a gleaming white creature out of a Renaissance fresco but as “flea-bitten and ragged. I kept saying, ‘She’s more of a cockroach or a monkey. There’s something feral and animalistic about her.’ ” Instead of flying around on wires the whole time, the actress playing the Angel is manipulated by six puppeteers in black.

The other breakthrough was having the action of the play, at the beginning, take place on three turntables, allowing for rapid location shifts; then, as the play goes on and gets more abstract, the turntables spin away and vanish.

“The play, for me, is about erosion,” Elliott said. “We strip away walls. We strip away revolves. We strip away anything that isn’t essential to the piece. And then we strip away illusions.” By the time Prior visits Heaven, late in “Perestroika,” the set has become the theatre itself. He pulls back a curtain—a “Wizard of Oz” reference—to find a team of angels working at lighting consoles and monitors, not unlike a stage crew during a tech rehearsal. “They’re trying to make things work back on Earth, as if it was another stage,” Elliott said. “And yet, of course, there’s no God. There’s no one person who is directing what should be happening down on the stage.”

All this was of interest to Tony Kushner. More than most living playwrights of his stature, Kushner is an open resource, sometimes to the vexation of his collaborators. “He’s very controlling, Tony, I have to say,” Elliott told me. “But, because of that, he’s also very generous.” “The World Only Spins Forward,” a new oral history of “Angels in America,” by Isaac Butler and Dan Kois, includes a section called “Tony Has Notes.” Declan Donnellan, who directed the first National Theatre production, in 1992, once received fifty pages from Kushner by fax in the middle of the night. Richard Feldman, who directed an early workshop at Juilliard, recalls getting a handwritten page that said, simply, “Ugh.” Kushner and Eustis had constant high-pitched fights during the original Los Angeles production, leading to a falling out; when the show moved to Broadway, in 1993, Eustis was replaced by Wolfe. (The stage directors’ union sued the New York producers, unsuccessfully, for retaining elements of Eustis’s production. Kushner and Eustis have since reconciled.) Wolfe had his own tangles with the playwright. “Part 1 was a baptism, because I got volumes and volumes of notes,” he told me. “But I did not retreat into a corner.”

The relationship between director and playwright is tricky, a combination of co-parenting and shotgun wedding. Eustis told me, “It can be very challenging for a director to work with Tony’s notes, because they tend to be infinitely more granular than most playwrights’. But he’s also a hell of a lot smarter than most playwrights.”

“I take a lot of notes,” Kushner said, when I met him at a steak house before a preview of “Millennium Approaches.” “Not nitpicky things, but I usually try to diagnose what I’m seeing.” He’ll scribble on a notepad in the dark, then type up his comments or dictate them to an assistant.

In the past quarter century, Kushner has worked on letting go. “I don’t like that side of myself,” he said. “There’s a narcissistic vulnerability that I don’t want to make anybody else’s problem. We’re seeing in the world right now what it feels like when somebody is unscrupulous about their narcissistic vulnerabilities becoming other people’s problems.” He stayed out of the way for most of Elliott’s twelve-week rehearsal period at the National, but the two e-mailed constantly. She would ask him about a specific line or phrase—including the meaning of “bubbeleh”—and often get a three-page response.