I was prowling the French Quarter one afternoon last August, when a food writer friend called with a tip to check out Jazz Tacos. On the way over, I stopped into a shop and mentioned that I was headed towards Exchange Alley. “There is a great restaurant there,” the shopkeeper said. “It’s called Jazz Tacos.”

Everyone was talking about Jazz Tacos. And why not? The cheery spot, with Mexican soap operas on the television and a smiling if harried Latino staff, served brightly flavored Mexican a...