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Ulysses’ home in Sharr White’s “Annapurna” is a grungy trailer set in the mountains of Colorado. Thomas A. Walsh’s set is so effective you can almost smell the mold and grim and whatever’s festering in the fridge. It’s a place that looks only slightly more inhabitable than that “magic bus” in Sean Penn’s “Into the Wild.” But if that pic’s young idealist had lived, he would definitely not be Ulysses. As embraced by Nick Offerman in a performance that’s breathtaking in several ways, there’s barely a breath of optimism left in this recluse-alcoholic-misanthrope-poet’s abused lungs.

Writing about a set is an odd way to begin a review. Then again, Walsh’s finely detailed work here tells you half of what you need to know about Ulysses, who left his wife and child 20 years ago. Actually, they left him. That’s the story, as well as the secret, of White’s two-hander, which begins when Ulysses’ ex-wife, Emma (Megan Mullally), pays him an extremely unexpected visit. She’s there to see him and clean up the place, although not necessarily in that order, and prepare him for the even more unexpected visit of his son.

We never get to meet the son. That’s the thing about two-handers: You often get the impression that the playwright has one eye on writing a very focused script and the other on getting it produced with as few actors to pay as possible. We should meet the boy, now 25 years old. And it is a credit to White’s powers as a writer that we feel we know him, as well as the many other relatives, neighbors, spouses and friends whom Ulysses and Emma recall on their way to exposing the real reason she and her son left 20 years ago.

Again, the word “breathtaking” describes Offerman’s performance. When we first see him, he’s there cooking sausage in a skillet and he’s nearly naked but for a dirty apron that does nothing to cover his butt. He’s got a gut and there’s hair on his back, and he’s clearly pissed that Emma’s intruded on his current solitude. Meanwhile, there’s also the irritant of Mullally’s voice, which is only slightly less treble than that of Karen Walker’s from “Will & Grace.” She’s complaining about her suitcases. Black out. Big laughs. In the next short scene, we notice that there’s also an oxygen tank on Ulysses’ back and a tube running into his nose. A couple more less hearty laughs about his cooking and being naked. Then another blackout. In the next scene, we finally notice the surgical patch on his chest. Offerman gives us a man who’s dying and isn’t going to accommodate one more thing or person or bad memory on his way to the end. It’s a powerful portrayal, and one that’s completely devoid of vanity.

His director, Bart DeLorenzo, clearly relishes the grotesque, and so does Offerman, who is much more the stage animal than Mullally, his real-life wife. Her “Will & Grace” voice, so effective in television, requires a few more notes to express Emma’s full rage and compassion. Mullally is, however, very moving when she reveals the play’s big secret in a monologue that recalls Martha’s ode to a son she never had in “Who’s Afraid of Virginia Woolf?”

Fortunately, Mullally never buckles to the too-easy laughter of the opening nighters who came to see a sitcom. Tennessee Williams once told a story about seeing Tallulah Bankhead in “A Streetcar Named Desire,” and how her fans wanted Tallulah and not Blanche DuBois, and how the actress finally caved to their demands. Thankfully, Mullally never caves at the Odyssey.

“Annapurna” was first presented in 2011 at the Magic Theater in San Francisco.

Annapurna

(Odyssey Theater Ensemble, Los Angeles; 99 seats, $30)

An Odyssey Theater Ensemble presentation of a play in one act by Sharr White. Directed by Bart DeLorenzo. Set, Thomas A. Walsh; costumes, Ann Closs Farley; lighting, Michael Gend; composer/sound, John Ballinger; props, Katherine S. Hunt. Opened and reviewed April 20, 2013. Running time: 1 HOUR, 30 MIN.

With: Nick Offerman, Megan Mullally.