The new musical “Cornelia Street,” set in a West Village café with its chef as the protagonist, boasts a number of promising ingredients. The libretto was written by acclaimed playwright Simon Stephens, the winner of Tony and Olivier awards for “The Curious Incident of the Dog in the Night-Time.” The production is being directed by estimable veteran Neil Pepe at his artistic home, Atlantic Theater Company, which has previously nurtured two of this century’s most enchanting new musicals, “Spring Awakening” and “Kimberly Akimbo.”

The cast is led by a two-time Tony winner, Norbert Leo Butz, making a welcome return to the musical stage in the role of the chef, Jacob, a middle-aged Jersey native who wears his dedication to a particular downtown New York ethos on his chest, by way of a Ramones T-shirt. (He’s also a Springsteen fan, we learn.)

While I hesitate to use Jacob’s professional parlance against him, “Cornelia Street,” despite its assets — which also include a set of compelling characters and other top-notch performers, from the venerable Mary Beth Peil to rising star Gizel Jiménez — seems a bit undercooked in this, its premiere presentation.

Perhaps a sharper metaphor would be a souffle that hasn’t fully risen. In musical theater, even with an intimate chamber piece like this one, musical numbers are supposed to represent heightened emotion; when characters break into song and dance, it should come across not as an arbitrary act, but rather as a necessary release. 

The music and lyrics for “Cornelia Street” were crafted by Mark Eitzel, Mr. Stephens’s collaborator on a couple of previous projects, who’s best known as co-founder of the alt-rock band American Music Club and a solo singer-songwriter. Mr. Eitzel’s Playbill bio informs us the Guardian has hailed him as “America’s greatest living lyricist,” but you’ll find scant supporting evidence in lines such as, “I always got a scheme/I always got a dream/You can’t lose with a gleam/In your eye” — Jacob’s declaration in the opening number, “The Good Life” — or, “The past is a shadow/Where you cling/But a rising tide/Is taking everything,” as his teenage daughter later laments in the darker “You Do Nothing.”

Mr. Eitzel’s melodies, which suggest recitative forever searching for an aria, do little to elevate these sentiments, though John Clancy’s orchestrations find moments of grace and nuance in them. The story, which follows Jacob and café owner Marty’s struggle to hold on to their place of business and the community it has helped sustain, carries a built-in poignance — especially for New Yorkers of a certain vintage, but also for anyone who has observed the fickle winds and callous overlords of real estate wreak havoc on a beloved neighborhood.

Under Mr. Pepe’s characteristically vigorous guidance, the actors make the members of this community vivid and, in most cases, endearing. It’s a pleasure to see, and hear, Mr. Butz apply his robust singing voice and gritty sardonicism to Jacob, a role that seems tailor-made for the performer at this stage of his career. The director’s daughter, Lena Pepe, makes a fetching off-Broadway debut as the teenager Jacob sired in a one-night stand and has raised alone, while Ms. Jiménez is plucky but palpably vulnerable as the grown daughter of a woman with whom Jacob had a longer relationship.

Kevyn Morrow brings an easy charm to Marty, Jacob’s comrade and sparring partner, while George Abud exudes a slick intensity as a taxi driver who frequents the café but turns out, in a jarring twist that Mr. Stephens doesn’t fully flesh out, to be more sinister than he appears. Jordan Lage chillingly inhabits a more recognizable villain, the real estate shark — dressed in workout gear for his one scene, where he deigns to visit the café, oozing bro-like jocularity — who Jacob thinks may be his savior, though we know otherwise from the start.

Yet no player or character better captures the essence of the disappearing world Messrs. Stephens, Eitzel, and Pepe are trying to evoke here than Ms. Peil’s Sarah, a woman of a certain age — about 20 years older than Jacob or Marty — who has kept the city’s ghosts and myths coursing through her veins, and is terrified by the prospect of losing them. In “Dance,” she reminisces about Studio 54, recalling the doorman who “let in the rich and famous/But he loved the ones who came to dance.”

The song is as cliché-ridden as others in “Cornelia Street,” but lifted up by the ensemble, it provides a transporting moment in a show that too seldom gets off the ground.