Preheat the oven broiler on high setting.
Slice the hoagie rolls lengthwise, ensuring the halves remain attached at the back hinge to hold the fillings.
Layer the deli turkey, salami, and pepperoni evenly on the rolls, then top the meats with the provolone cheese slices.
Place the open-faced rolls on a baking sheet and broil for 2 to 4 minutes until the cheese is melted and bubbling and the bread edges are toasted.
In a large mixing bowl, whisk together the mayonnaise, red wine vinegar, minced garlic, dried oregano, red pepper flakes, and Parmesan cheese to create the grinder dressing.
Add the shredded iceberg lettuce, sliced red onion, and pepperoncini peppers to the bowl and toss thoroughly until the salad is evenly coated.
Remove the toasted sandwiches from the oven and place the sliced tomatoes over the melted cheese, seasoning them with a pinch of salt and pepper.
Pile a generous portion of the dressed grinder salad onto the meat and cheese side of each sandwich.
Fold the sandwiches closed, press down firmly to compress the salad, and slice diagonally before serving immediately.