Progress Grocery is a deli that serves great Muffulettas. Seating is available in the front of the store, or take it to go.
A muffuletta is an interesting food, and one is large enough to feed two hungry adults. It's made with a large bread-type thing, somewhere between a round loaf of bread and a pita. There's cheese, lunch meat and a thick layer of olive salad.
The Progress Grocery version of the muffuletta is lighter (but still not a diet food) than the original found two doors down. Try one of these - it's a requirement to make your visit to New Orleans complete.