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Despite an earthily authoritative turn by Ernestine Jackson (now replaced by Jackie Richardson) as fabled blues artist Alberta Hunter, Cookin’ at the Cookery doesn’t actually start cookin’ until about 45 minutes in. That’s when trumpet-toting Louis Armstrong drops by to sing a duet with Hunter, lending his toothy grin and a little starpower to an evening that seems determined to diminish its leading lady even as it celebrates her.

Hunter had a remarkable life, singing with everyone from Fats Waller to Paul Robeson, becoming one of the better-known African-American entertainers of the 1920s, marrying verrry briefly (she was a lesbian), and touring Europe and the Pacific well into the 1950s. Then, after a two-decade hiatus, during which time she “invented” a high-school diploma and became a full-time nurse, she sprang out of retirement to knock a new generation of audiences dead at the age of 82.

All of which suggests a woman far more intriguing than the conventionally spunky creature that writer/director Marion J. Caffey has put onstage in Cookery. Admittedly, the music is plenty engaging as sung smokily and with ample wit by Jackson, whose voice is considerably prettier and more supple than Hunter’s ever was. Restricting her for most of the evening to a low, bluesy register will seem criminal to anyone who heard Jackson send melodies soaring in Raisin and Guys and Dolls three decades ago. But the real crime is asking her to mouth the hopelessly flat-footed interstitial dialogue (“My mother’s dead; I forgot to check; damn, these are the blues”) with which Caffey keeps interrupting the music. To hear him tell it, Hunter’s life story would barely fill one column of liner notes on a greatest hits CD.

So count it as faintly disconcerting, if refreshing, when Satchmo arrives to upstage the blues legend in her own show. He’s played by diminutive dynamo Janice Lorraine, who’s been mugging to beat the band all evening as everyone from 9-year-old Alberta (think Shirley Temple crossed with Betty Boop), to stooped, ancient restaurateur Barney Josephson, proprietor of the East Village nightspot where Hunter made her fateful comeback.

Finally handed a character with a real-life persona as broad as her impersonations (and momentarily freed from the need to offer explanatory dialogue about who he is, or what he’s done), Lorraine manages in a few seconds to do for this jazz-world interloper what everyone’s been trying so hard all evening to do for Hunter. She flashes Satchmo’s familiar toothy grin, growls the first few words of “When the Saints Come Marchin’ In” in perfect mimicry of his guttural rasp, and damned if the whole place doesn’t just light up.