Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
Slice the hoagie rolls lengthwise, ensuring they remain attached at the back hinge.
Spread a thin layer of mayonnaise on the interior of each roll.
Layer the salami, ham, pepperoni, and capicola evenly across the four rolls.
Top the meats with two slices of provolone cheese per sandwich.
In a small bowl, whisk together the melted butter, dried oregano, and garlic powder.
Close the sandwiches and brush the tops of the rolls with the seasoned butter mixture.
Place sandwiches on the prepared baking sheet and bake for 10 minutes, or until the cheese is melted and the bread is golden brown.
Remove from the oven and carefully open the sandwiches to add lettuce, tomato, onion, and banana peppers.
Drizzle with Italian vinaigrette, close the sandwiches, slice diagonally, and serve immediately.