“I do like to write sinister but quite funny guys, who can combine a sense of menace and danger but also real loss,” Mr. McDonagh said by phone. “Carmichael is all of that, but he’s also someone who is very, very honorable in his own crazy way, with a moral code that gets crossed by people. Chris is so ideal in this role, because he’s so funny but can turn to that dark side on a dime, and because he can see the niceness in these odd people.”

Beyond bringing Mr. Walken back to the stage  he was last seen in 2000 in a Tony-Award-nominated performance in the musical “James Joyce’s The Dead”  Carmichael also stands out as one of several strong-willed male characters on Broadway this spring, a year after a season of imperious female roles (“Mary Stuart,” “33 Variations,” “Irena’s Vow,” “Blithe Spirit”). The forthcoming plays “Enron” (with Kenneth Lay and Jeffrey Skilling as characters), “Next Fall,” “Fences” and “Red,” as well as the musicals “American Idiot,” “Million Dollar Quartet” and “La Cage aux Folles” all feature men of fire-tested mettle who are grappling with identity, obsession, failure and mortality.

There is no particular rhyme or reason to Broadway being busier for one sex or the other; rather, it’s all about commercially viable shows. Some of these plays were big hits in London, while some of the musicals are set to proven hit songs. And, of course, there are always the shows with star performers to help sell tickets, like Mr. Walken in “A Behanding in Spokane.”

While the script of “Behanding” calls for Carmichael to be in his mid to late 40s, Mr. McDonagh and the director, John Crowley (“A Steady Rain,” “The Pillowman”), said they had trouble finding actors that age who were suitable for or interested in the role, which is part of an ensemble, in this premiere production of the play.

The two men discussed needing someone like Mr. Walken, who is known for quicksilver film performances  the young man in love who becomes a Russian-roulette-playing soldier in “The Deer Hunter” (1978) or the deceitful but loving father in “Catch Me if You Can” (2002). (Mr. Walken was nominated for Academy Awards for best supporting actor for both roles, and won for “The Deer Hunter.”) The new role also comes with important monologues that feature bizarre twists similar to the rambling speech Mr. Walken delivers as Captain Koons, who tells the story of a gold watch to a young boy in “Pulp Fiction” (1994).

So the playwright and director asked each other, why not cast the man himself?

“Whereas some other actors felt that Carmichael was far-fetched, Chris didn’t feel the far-fetched elements were odd at all,” Mr. Crowley said. “And I think the fact that Chris is 66 throws into stronger relief that finding his hand has been a lifelong quest, a function of the character’s neurosis. And that the journey is more important than the destination.”

Image Blair Brown and Christopher Walken in “James Joyce’s The Dead” in 2000. Credit... Sara Krulwich/The New York Times

“The most surprising thing that Chris does,” he continued, “is that while he has this ambient, freaky, chilling quality that curls around him, he can also plug into a character’s vulnerability in a split second with his face, his tone, his body.”