These gigantic sandwiches were invented a century ago at Sicilian Deli here in New Orleans. The spicy, tangy olive salad is what really sets this meat and cheese sandwich apart. A genuine muffuletta should be made on oven-fresh Italian bread topped with sesame seeds. Be sure and use the highest-quality ingredients available; it really makes a difference! Since you’re going to all the trouble of making the olive salad, consider doubling the recipe so you’ll have some extra waiting around for when you get another muffuletta craving — it keeps for at least a month! Note: Use round bread loaves for real muffuletta.https://centralmarket.com/

Italian Olive Salad ( Homemade ore store bought)
2 (1 pound) loaves Italian bread
8 ounces thinly sliced Genoa salami
8 ounces thinly sliced cooked ham
8 ounces sliced mortadella
8 ounces sliced mozzarella cheese
8 ounces sliced provolone cheese

To Make Sandwiches: Cut loaves of bread in half horizontally; hollow out some of the excess bread to make room for filling. Spread each piece of bread with equal amounts olive salad, including oil. Layer ‘bottom half’ of each loaf with 1/2 of the salami, ham, mortadella, mozzarella and Provolone. Replace ‘top half’ on each loaf and cut sandwich into quarters.
Serve immediately, or wrap tightly and refrigerate for a few hours; this will allow for the flavors to mingle and the olive salad to soak into the bread.

https://www.amazon.com/Boscoli-Olive-Salad-32-oz/dp/B001HBRDVU/ref=pd_lpo_1?pd_rd_i=B001HBRDVU&psc=1

This sandwich actually came from my local grocery store . They back homemade Italian bread and make homemade Olive salad which you can purchase or the sandwiches.

Cannatella’s Grocery & Hardware

Cannatella’s Grocery is a fourth-generation grocery and hardware store that has been serving the people of Melville since 1923. The store carries general merchandise, lumber, and a wide variety of tools and hardware. On the grocery side, you can purchase a freshly made muffuletta, fresh Italian sausage, or their famous olive salad, all recipes that have been in the Cannatella family for ages.

While visiting, be sure to browse The Old Store, which is adjacent, to see photos and items from the past, including the original pressed tin ceiling. Also, shop for antique and vintage items.