Whisk the first 3 ingredients in a large bowl to blend. Gradually blend in the oil. Stir in the olives and roasted peppers. Season the vinaigrette, to taste, with salt and pepper.
Cut the top 1-inch of the bread loaf. Set the top aside. Hollow out the bottom and top halves of the bread. Spread some of the olive and roasted pepper mix over the bread bottom and cut side of the bread top. Layer the meats and cheeses in the bread bottom. Top with the onions, then the arugula. Spread the remaining olive and roasted pepper mix on top of the sandwich and carefully cover with the bread top. You can serve the sandwich immediately or you can wrap the entire sandwich tightly in plastic wrap and place in the refrigerator a day before serving.