Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with foil or parchment paper.
Place sliced rolls on the prepared baking sheet (if the top half of roll rocks from side to side too much, slice a tiny bit of the top off). Place 1 slice of provolone on each slice of bread. Tear up the remaining slice of provolone to cover any open bread areas.
Bake in the preheated oven until melted (not browned), about 8 minutes. Remove from oven; leave the oven on.
Fold two pieces of turkey onto two slices of bread. Fold two pieces of ham onto the other slices of bread.
Layer 2 slices of soppressata on top of the turkey. Fold 2 slices of prosciutto onto ham. Place four pepperoni pieces on top of each bread half.
Sprinkle slices with some of the Parmesan cheese. Place back into the oven and let bake until pepperoni is looking crispy, about 12 minutes.
While slices bake, make the grinder salad. Add mayonnaise, red wine vinegar, garlic, oregano, salt, pepper, and pepper flakes to a bowl. Whisk to combine.
Add lettuce, onion, and pepperoncinis to the dressing. Toss to coat.
Remove sandwiches from the oven. Top 2 of the ciabatta slices with tomato slices. Using tongs, place a layer of salad on top of the tomatoes. Sprinkle with more Parmesan cheese.
Place the non-salad slices on top of the salad ones. Cut each sandwich in half and serve.
