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Contrary to what the name may suggest, this food has nothing to do with muffins. Muffuletta can refer to a light type of bread similar to focaccia or a type of sandwich. The sandwich has a long history in New Orleans, tracing its roots back to 1906, when it was invented at Central Grocery & Deli. It’s typically stacked with cured meats, cheese, and olive salad for a briney, hearty dish.