Slice the Hawaiian buns open horizontally and lay the bottom half on a 9 x 13 cookie sheet.
In a medium bowl, combine the lettuce, tomatoes, red onion, and pepperoncini peppers. Add the mayonnaise, red wine vinegar, and spices, and stir well to coat the salad ingredients.
Start building the sandwiches by layering the ham, pepperoni, salami, and provolone cheese. Add the top layer of buns and cut through the sandwiches between the rolls. Lift the top layer of buns and add the salad topping.
Replace the top buns, cover, and chill until ready to serve.