The real-life couple play Ulysses (Offerman) and ex-wife Emma (Mullally); he's preparing for the end of his life just as she tracks him down, and they fall quickly back into the rhythm of dialogue that only an actual couple could replicate. Intensity builds throughout the play, leaving many audience members in tears as the lights come back up.
"Being a person who is mostly known for comedy, I've never had the experience of people audibly weeping at the end of our show," Mullally, 55, tells PEOPLE. "It's really kind of great. I don't want to upset anyone, but it's great that the show is effective enough to bring out emotions."
Offerman and Mullally, who've been married since 2003, decided to bring the play to New York after a successful run in Los Angeles last spring. The decision to work together seems to have been an easy one for the pair, who've costarred several times on Offerman's NBC series, Parks and Recreation.
"When Megan came on Parks and Rec as Tammy 2, that was kind of a watershed moment for me where we were treated like peers, like a team," Offerman, 43, recalls. "Up until that point I'd felt like Megan's student and fan. So once that happened, those particular roles required a lot of trust and vulnerability to go to horrifyingly deep places, especially with our tongues. So I feel like we've graduated to a level where we can look at each other and jump off any cliff together."
"There is a nice sort of security working together, but I also feel like we're more relaxed," Mullally adds.
This staging of Annapurna came about a few years ago, when Mullally and Offerman both found themselves in the mood to do a play. The Odyssey Theatre Ensemble of Los Angeles found the script – the show had only been produced once before – and passed it along to the stars. "We said, 'Well that's a happy accident – it's a two-person play and both parts are right for us,'" Mullally recalls. And the rest is now history – or will be once Annapurna finishes its seven-week run.
As for future plans, Mullally hints that they have "a few ideas in the works," including a television show and a movie. But for now, they're enjoying their time in New York City – and missing their dogs, who are at home in L.A.
"We were going to bring them here originally but decided that it would be fun for us, but not so much for them," Mullally says. "We just have to grin and bear it. But our assistant is sending us adorable photos."
Annapurna runs through June 1 at New York's Acorn Theatre.