In “Fat Ham,” James Ijames’s Pulitzer Prize-winning, rip-roaringly funny adaptation of “Hamlet,” something is rotten in the state of North Carolina — though as Mr. Ijames has drily noted in the playbill, the setting “could also be Virginia, or Maryland or Tennessee. It is not Mississippi, or Alabama or Florida. That’s a different thing altogether.”

You needn’t be an expert on regional differences in the American South to savor this inspired comedic makeover of an iconic tragedy, which had its New York premiere at the Public Theater last year. Director Saheem Ali, who has earned acclaim for his innovative takes on actual Shakespeare works, has brought the production uptown with its exuberant irreverence and splendid cast — many of the latter Broadway newbies — very much intact.

Marcel Spears anchors the ensemble as Juicy, the Hamlet figure, a Black, gay young man studying human resources through the University of Phoenix’s online program. Early in the play, Juicy is visited by the ghost of his Pap, made explosively earthy by the redoubtable veteran Billy Eugene Jones; imagine Hamlet’s father if his kingdom had been a barbecue restaurant, and he had belittled his son throughout his life as, to borrow a couple of epithets from their opening exchange, a “pansy” and a “girly a– puddle of spit.”

Pap nonetheless wants his son to do him a big favor, and murder his brother and Juicy’s uncle, Rev — also portrayed by Mr. Jones — who has already taken up with Pap’s sexy widow and Juicy’s mother, Tedra, played by a delectable Nikki Crawford to suggest J. Lo on speed. That adds Claudius and Gertrude to the mix, if you’re keeping track; there are also variations on Horatio, Polonius, Laertes, and Ophelia, though Juicy’s sexual orientation is just one of many factors that make some character dynamics, like the characters themselves, different. 

In fact, you don’t need to have read “Hamlet” or seen a single production, or film version, to enjoy the heights of raucous hilarity reached by Messrs. Ijames and Ali and the actors, or the depths of poignance that accompany them from time to time. Predictably, the boorish, conniving Rev deals with Juicy just as brutally as his Pap did, and while Tedra plainly adores her son, she does little to protect him.

Mr. Spears’s delightfully airy delivery, all detached erudition and dry mockery, keeps Juicy raised above the fray to a point, and drives home the extent to which his character parodies Shakespeare’s pensive prince. “I’m an empath,” Juicy declares, deadpan; he adds, “I can’t help who I am. I ponder.” Yet the actor and the play make it clear that our hero is not inured to the cruelty surrounding him; Mr. Ijames also artfully injects Shakespearean language as Juicy confronts his current dilemma — to kill or not to kill his uncle — and contemplates all his family baggage. 

Juicy gets some cheekier references to the text of “Hamlet,” as do others, like his cousin Tio, a porn-addicted stoner whose buzz is captured to wacky perfection by Chris Herbie Holland. More giddiness, and conflict, ensue at Rev and Tedra’s wedding party, an outdoor cookout infused with ironic exuberance by scenic designer Maruti Evans, where guests include the flamboyantly pious Rabby and her rebellious daughter Opal, respectively played by a pistol-sharp Benja Kay Thomas and an exquisitely piquant Adrianna Mitchell.   

Calvin Leon Smith is more subdued, at least initially, as Opal’s brother, Larry, a military man who on the surface seems to embody both Rabby’s conservative ideals and Rev’s cartoonish, backward notion of masculinity. Larry is a bemused observer during a priceless karaoke sequence, when Juicy, pressed into taking part, performs Radiohead’s brooding, navel-gazing anthem “Creep” — because, well, what else would a modern-day Hamlet sing, at least if choosing from a period of pop music before Coldplay and after The Smiths?

A twist near the end of “Fat Ham” lays the foundation for another musical number, this one unironically and deliriously upbeat. It’s certainly not the kind of catharsis you’d expect from an Elizabethan tragedy, but like the production itself, it’s scrumptious and utterly satisfying.