Prep. Line a baking sheet with aluminum foil and preheat the oven to 350°F.
Make the sauce. Whisk together the butter, Italian seasoning, and pepper.
Toast the hoagie rolls. Open the hoagie rolls and place them cut-side up on the prepared baking sheet. Brush the sauce over both sides of each roll. Bake for 7 minutes or until golden brown.
Load the sandwiches. Remove the rolls from the oven and arrange 3 slices of soppressata, 3 slices of salami, and 3 slices of prosciutto inside each roll. Top the meat with 3 slices of mozzarella (per sandwich) and a sprinkle of parmesan.
Bake. Gently close the rolls, wrap each sandwich in foil, and bake for 15 minutes or until the cheese has melted.
Add toppings. Gently open the sandwiches and top with lettuce, tomato slices, and pepperoncini. Close the sandwiches.