Prepare the Olive Salad: In a medium bowl, combine the chopped green olives, black olives, roasted red peppers, and giardiniera. Drizzle with olive oil and, if using, red wine vinegar. Season with salt and pepper to taste. Mix well and let sit for about 30 minutes to marinate.
Slice the Bread: Using a serrated knife, carefully slice the round loaf of Sicilian bread in half horizontally, creating a top and bottom. Remove a small amount of the soft bread from the center to create a little hollow.
Layer the Sandwich: Begin layering on the bottom half of the bread. Start with the salami and ham, followed by the mozzarella and provolone slices. Then, add the prepared olive salad evenly over the cheeses.
Top It Off: Place the top half of the bread on the sandwich. Press down gently to help the ingredients meld together.
Wrap and Refrigerate: Wrap the sandwich tightly in plastic wrap and place a heavy skillet or cutting board on top to compress it. Refrigerate for at least an hour (or overnight for better flavor).
Serve: When ready to serve, unwrap the sandwich and slice into wedges or halves. Garnish with fresh basil leaves.