Things You'll Need
Find the right bun. The Sicilian sesame seed bun is a hard to replicate. The Central Grocery bun is baked with a sheen of olive oil or sesame oil on the surface. Seeded Italian bread, preferably from an Italian bakery, could serve as a valid substitute.
Split open the Italian bun. Spoon the olive salad onto both sides of the bread. Spread the cheese slices across the bottom bun piece.
Add the layers of meat over the cheese. The meat and cheese should combine to weigh about 1/4 lb.
Cut the sandwich into 4 or 8 pieces, and tightly wrap each piece in plastic wrap. Put the pieces into the fridge, and let the olive salad and meats marinate together overnight. The sandwiches can be served cold or heated.