In September,Chef Greg Sonnier returned from a frustrating trip to City Hall, hung a “For Sale” on the banquet facility he had purchased Uptown on Henry Clay Avenue and Laurel Street and decided he would never be able to reopen Gabrielle Restaurant. After a few weeks, Sonnier changed his mind. “I can’t give up on New Orleans,” he says. “I’ve been here my whole life.”

Sonnier, along with his wife Mary, ran Gabrielle in Mid-City for 14 years, garnering national...