Who would have thought that the most compelling musical comedy heroine in decades would be a nearly 100-year-old cartoon character?

I’ll admit I didn’t know quite what to expect upon arriving at the Broadhurst Theatre to catch a preview of “BOOP! The Musical.” The show’s librettist, Bob Martin, has helped create such exuberantly entertaining works as “The Drowsy Chaperone,” “Elf,” and “The Prom,” and the new production is directed and choreographed by Jerry Mitchell, whose many celebrated credits include “Kinky Boots” and “Legally Blonde,” so I expected it would be cleverly and lovingly executed.

Still, I wondered how these Broadway veterans and their collaborators could cull a two-act musical from the adventures of Betty Boop, the curvy, doe-eyed animated figure who became a screen sensation in the 1930s. What I didn’t consider is how Betty evolved over that decade: Arriving as a voluptuous but girlish flapper who catered to sexist stereotypes while also embodying sexual independence, she was forced into a more constricted role after the Hays Code of 1934 instituted a new puritanism in the motion picture industry. 

The Betty we meet in “BOOP!” skews more closely to her original incarnation, the Jazz Age baby. Leading lady Jasmine Amy Rogers, in a star-making performance, models sexy, glittering costumes by Gregg Barnes and boasts a million-dollar giggle. When Betty is propelled from the black-and-white world of her Fleischer Studios set into the vivid color of modern-day New York City — a journey charted to spectacular effect by the scenic, lighting, and projection design of, respectively, David Rockwell, Philip S. Rosenberg, and Finn Ross — she thinks she’s escaping the trappings of celebrity.

Instead, our protagonist finds herself faced with the challenges of flesh-and-blood womanhood. Rather than simply getting chased by cartoon men (“Then I knock ’em out with whatever’s at hand,” she explains at one point), Betty finds herself grappling with a real-life bully and making a true friend. And yes, she falls in love — with a guy who admits he hasn’t seen any of her movies. (“They’re called shorts,” she notes, correcting him.) 

Messrs. Martin and Mitchell, Ms. Rogers, and Susan Birkenhead, a veteran musical theater lyricist — teamed here with David Foster, a composer who has been writing and producing pop hits for nearly half a century — follow these developments with humor and heart; and they can provide more insight, in their giddy fashion, than many more serious-minded accounts of women’s issues, in theater and other mediums. 

That said, “BOOP!” is first and foremost exhilarating, enchanting entertainment. Mr. Mitchell and his designers open the show with a dazzling production number, featuring a scrumptiously attired, tap-happy chorus line and witty special effects, and neither their energy nor their imagination flags over the roughly two and a half hours (including an intermission) that follow.

Ms. Rogers, hilarious and charming throughout, also captures Betty’s budding humanity, so that you can feel the anxiety and wonder in her speaking and singing, which both expertly mimic the character’s baby-doll voice. The actress receives winning support from the other players, among them Faith Prince, a musical theater stalwart who more than 30 years ago triumphed as another feisty, resilient heroine, Miss Adelaide, in a revival of “Guys and Dolls.”

“BOOP!” casts Ms. Prince as one Valentina, an astrophysicist who meets Betty’s professorial Grampy, played with endearing goofiness by Stephen DeRosa, as both are traveling through dimensions, and becomes a wonderfully warm, spicy partner. Angelica Hale is adorable as Trisha, a precocious but insecure teenager who befriends Betty after being a fan, and Erich Bergen preens and schemes amusingly as Raymond Demarest, a mayoral candidate who preys on Betty in various ways — to no avail, of course.

As Betty’s love interest, Dwayne, Ainsley Melham enjoys a relaxed, pleasing chemistry with Ms. Rogers. No character here proves more eager for Betty’s affection, though, than her cherished dog, Pudgy, represented by a marionette; crafted and maneuvered by Phillip Huber, this is the cutest and funniest puppet to land on Broadway since the model of Milky White that pranced and mooed through a 2022 production of “Into the Woods.”

Like the people we meet in “BOOP!,” both those born and those drawn into existence, Pudgy is ultimately able to straddle worlds through the power of love. That may sound corny, but I’d jump to revisit this delightful bunch in any realm.