Make the olive salad: Add the olives, red peppers, capers, pepper, Italian seasoning, celery seeds, red pepper flakes, and giardiniera to a food processor and pulse until coarsely chopped. Transfer to a medium bowl and whisk in the olive oil. Cover and set aside.

Make the muffalettas: Cut off the top 1/3 of each boule and set aside. Carefully remove the inside of the loaf, leaving about a 1/2 inch thick layer of bread behind. Reserve the bread scraps for another use.

Add a large spoonful of olive salad to the bottom of the bread bowls and spread evenly. Layer 4 slices of salami, 4 slices of mortadella, 4 slices of sopressata, and 2 slices of provolone in each loaf. Top with another layer of olive salad and spread evenly. Cover with the bread tops. Cover tightly with plastic wrap and refrigerate for at least 4 hours, up to overnight.

When ready to serve, slice the muffalettas into quarters.