NEW YORK — Ignore the cynics and their interest in intimidating ironic innovation! With the market tanking and worry exploding all around, affordable escapism soon will be having a boffo moment at the Broadway box office. Enter at the Broadhurst Theatre a joyous, retro, family-friendly charmer for a discombobulated world. Director Jerry Mitchell’s sing-and-smile-along production of “Boop! The Musical” is like gulping a glass of fizzy sangria after a rough day, heck, after a rough three months and counting of stress and strife.

What’s not to love about Betty Boop, U.S.-based international ambassador? It’s a rhetorical question, folks. She cannot be fired.

Vastly improved from its Chicago tryout — Mitchell being a master of the dogged retrofit — “Boop!” is now a stellar little showcase for its ascendant young star, Jasmine Amy Rogers, who does not let playing a literal cartoon character get in the way of a fully fleshed out performance, as sweet and vulnerable as it is determined and resolute.

Still in her mid-20s, Rogers might not yet be a match for Broadway’s biggest divas. But she sings and dances her alter ego’s oversized head off, fully at ease with David Foster’s lush and muscular score and Susan Birkenhead’s amusing lyrics. More importantly, she fully understands what it means to play a character who has spent the last century or so hanging on in the face of formidable Disney competition.

She might have played Snow White before Rachel Zegler and shown her chops as a lion tamer, but Betty Boop had to emerge from Max Fleischer film shorts, not Uncle Walt’s theme parks. She had to stay relevant all these years through her own sex appeal, not decades of marketing campaigns. And she somehow has stuck around the zeitgeist even though she mostly spent her previous screen time running away from aggressive men.

Deftly ignoring the little matter of her being a line-drawn cartoon, Bob Martin, the show’s book writer, picks up on the idea that Betty must have become sick of those same vampish plot points, and forges a show wherein Ms. Boop undergoes a kind of early midlife crisis and craves a vacation.

Thus she exits her black-and-white world via a time machine crafted by sidekick Grampy (Stephen DeRosa) and ends up, of all places, at the Javits Center in the middle of New York Comic Con, where she quickly sees that she enjoys a certain immortality. Apparently, seen-it-all New Yorkers have no issue with a 100-year-old cartoon icon coming to life before their eyes.

Thus Betty’s New York adventures then include falling in love with Dwayne (Ainsley Melham), acting as a surrogate mom to the spunky teenage Betty fan Trisha (Angelica Hale, another delightful Mitchell discovery) and maybe even steering New York away from the wrong ascendent mayoral candidate (Erich Bergen) by persuading Trisha’s mom Carol (Anastacia McCleskey) to run for mayor herself. All in a day’s work, even as Grampy is distracted by his relationship with Valentina, another of the musical’s actual Boop characters, now played in a cameo by the veteran musical-comedy star Faith Prince, a piece of casting that centers this show familiar within long-standing and thus comforting Broadway traditions.

Mitchell figured out that it says Betty Boop on the marquee and he excised a hefty chunk of the old Chicago caper plot in favor of giving as much stage time to Rogers as possible. Excellent choice. Audiences eat her up, as they do Hale’s Trisha and the puppet pooch Pudgy, as wrangled by Phillip Huber. Like everyone else, the dog starts out in black and white, only for his schlerping tongue to gain some technicolor.

The big Act 1 closer is a stellar Foster production number, “Where I Wanna Be,” a fine showcase for this dance-forward show. Along with “Why Look Around the Corner,” a ball-bouncing singalong, that’s the anchor of Foster’s score, a populist, filmic and romantically orchestrated song suite that only has one relative misfire, the eleven o’clock number, “Something to Shout About.”

“Where I Wanna Be” is actually an apt descriptor of the entire show: a confident mid-range musical when it comes to size and spectacle, an unabashedly family- and visitor-friendly attraction and an old-school romantic comedy. If it finds its intended international audience, the cameras will keep whirring on Betty. The show also functions very much as a love letter to that devil’s playground called Times Square, where Betty finds characters that look like her but have even bigger noggins. They function as their own executioners, too. She finds that strange. As do we all.

Self-evidently, one has to overlook some illogicalities here, but Rogers makes that easy. The set designer David Rockwell and costume designer Gregg Barnes both have a lot of fun with the assignment but they also keep things disciplined. Shows like this often fall off the tracks when they reach too far, keep breaking their own rules or let spectacle steal humanity.

Here, Betty does not allow any of that to happen.

Thus “Boop!” builds and communicates its own optimistic world, inhabits it fully and makes no apology to anyone. No “Boop-Oop-a-Doop” is necessary.

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At the Broadhurst Theatre, 235 W 44th St., New York; boopthemusical.com.

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