1. Cut the loaves of bread in half lengthwise, and arrange them in a single layer, cut sides up. Liberally brush the bread with the vinaigrette. On the bottom half of each loaf, evenly layer one-quarter of the provolone, followed by one-quarter of the mortadella, one-quarter of the spicy ham, and one-quarter of the salami. Top with 2 slices of tomatoes and 3 slices of onion. Divide the cherry peppers among the sandwiches. Stir the vinaigrette and generously drizzle it over the onion and tomato.
2. In a small bowl, toss the torn lettuce with some of the remaining vinaigrette. Divide the lettuce among the 4 sandwiches, top with the other halves of the bread, and serve.
1. In a small mixing bowl, combine the balsamic vinegar, basil, oregano, and garlic; whisk well to mix. Continue whisking while slowly drizzling in the olive oil in a slow, steady stream. Add the salt and pepper, and whisk to combine.
2. The vinaigrette may be stored in an airtight container in the refrigerator for up to 1 week.