The most controversial cabaret in town might be happening at the August Wilson Theatre, but the best one is at the Lyceum. There, Cole Escola’s riotous, extremely faux-historical farce, Oh, Mary!, has begun its Broadway run, and long may it reign. Oh, Mary! took the West Village deliriously captive in its big gay pirate ship back in the spring, and while the wickedly clever Escola — who made their name first on YouTube playing wonderfully unhinged characters, then as a scene-stealer on shows like Search Party and Difficult People — is on record calling the uptown transfer “a mistake,” they and director Sam Pinkleton have wisely left funny enough alone. Really, far more than enough — Oh, Mary! is hilarious and, underneath the mayhem, both structurally rock solid and sneakily moving. It may be playing the palace now, but it’s confident enough in its own skin to have resisted any sort of unnecessary makeover.

This lack of dolling up for Broadway doesn’t just serve the show as an already A+ piece of comedy; it’s also in keeping with the thematic heart of the whole project. Though it’s always possible to enjoy a romp as wild and wily as Escola’s purely for its zany twists and shameless cackles, Oh, Mary! isn’t about nothing. What is has to say (beneath the “bratty curls,” bouncing hoop skirts, and spit-take-inducing jokes about inbreeding) is that you’ve got to find your parade, as freaky or frightening as it might be, and refuse to let anyone rain on it. It is, in essence, a liberation story, a celebration of funny girls of all stripes, of self-actualization beyond the oppressive confines of social normativity and cultural — big air quotes — “legitimacy.”

Though she’s not exactly Edna Pontellier, Escola’s Mary Todd Lincoln is in desperate need of an awakening. Or, perhaps more accurately, a reawakening. Mary — the suffering wife of the 16th president, driven by the ruthless tedium of her life to rampant alcoholism and diabolical abuse of her goody-goody companion, Louise (Bianca Leigh) — once had hold of her joy, her purpose, her true identity, and she lost it. She’s a wing-clipped bird who, in marrying Honest Abe, gave up “the thing I love more than anything on earth … cabaret!” Escola, as both writer and actor, is the kind of utterly alert, funny-to-the-fingertips comic savant who probably took exactly the right length of beats before coming out of their mother’s womb. When their Mary announces her life’s great passion, or reminds her husband that “people traveled the world over for my short legs and long medleys,” or — as she begins acting lessons with a worrisomely hunky teacher — launches into a burring, lisping, writhing delivery of iambic pentameter that makes her sound like “a horny snake,” she is, for all her diegetic disempowerment, in total control of us. If Escola says, “Laugh,” we say, “How loud — and with how much danger of peeing a little?”

Among Oh, Mary!’s triumphs, though, is that the production isn’t simply the Cole Escola Show. Pinkleton’s direction is unflaggingly madcap — like the bus in Speed, it never drops below 50 miles per hour (really, more like 70). And while the cast spends quite a bit of the show’s 90 minutes shouting, we never tire of the cranked-up volume or the fever pitch. There’s an appreciation for melodrama of all modes and eras — from Boucicault to Charles Busch to Liza Minnelli — built into the material, and Escola isn’t the only one with a knack for it. Leigh is a hoot as the prim, flouncing Louise, who harbors a dirty little secret involving ice cream; Tony Macht is completely dear in the show’s most innocent role, a diligent young soldier named Simon with a crush on mad Mary; and James Scully goes from very good in his scenes as Mary’s hot drama teacher to straight-up brilliant when the plot twists him into the position of psycho ex-boyfriend. Meanwhile, Conrad Ricamora’s maniacal, hopelessly conflicted Abraham Lincoln has only gotten sharper and more released since I saw the show downtown. Crucially, though he rails at Mary and hides her booze; brutally laments their marriage; and plots to subdue, humiliate, and even institutionalize her, he is not solely her enemy. What he is, really, is a fellow sufferer whose violent denial of self has led him into hell. He’s Joe Pitt in wolf’s clothing and a stovepipe hat. Though he claims to loathe the genre Mary loves, we know he met his wife when he saw her on the cabaret stage, and something about all that jazz must have called to him. “I don’t love cabaret! Stop saying that!” he roars at Mary. “It makes me look like a … like a fffff …” Ricamora chokes expertly on the f, but Escola is right there to pick up the ball as Mary, ever defiant, hollers her response: “Like a what? Like a fffffan of elegant stories told through song?”

In the end, it’s not his wife Abe hates but himself. If he takes his cruelty out on Mary, it’s because she doesn’t share his skill for repression. Who she truly is — the monster, the weirdo, the aspiring heart, the glorious singer of “madcap medleys” — is always right there, just under the surface, fighting and clawing to escape the yards of black taffeta, the whalebone stays, and every other form of cage. Abe put a headstone atop his honest desires long ago, but Mary’s can’t be killed, no matter how much liquor she attempts to drown them in.

Not only does Mary herself put on one hell of a show, it’s also a joy to see Escola — who dropped out of college after one year because they couldn’t take out more loans, and who turned their own very real suffering into such generous flights of hilarity — kick down the doors of what Ricamora’s Abe Lincoln calls, with a pompous sniff, “the legitimate theater.” Sometimes, the most loving creations are the least reverent. And, as Mary so convincingly proclaims to her husband, “There’s no difference between theater and cabaret. Theater is just fewer feathers and flatter shoes!” As for the serious stuff, if you’re wondering whether Oh, Mary! takes us all the way up to the big bang at Ford’s Theatre, I’ll simply say you should visit the Lyceum to find out. After all, what good is sitting alone in your room?