Prepare the grinder salad by combining mayonnaise, apple vinegar, garlic powder, oregano, salt, and pepper in a large bowl. Whisk until smooth.
Mix in the shredded iceberg lettuce, sliced red onion, and banana peppers to the mayo mixture and stir gently.
Slice open each sub roll and divide the turkey slices, turkey pepperoni, and turkey among them. Layer provolone cheese on top.
Place the assembled sandwiches under the broiler for about 2–3 minutes until the cheese is melted and bubbly.
Top each sandwich with fresh tomato slices and season with salt and pepper.
Spoon a generous amount of the prepared grinder salad onto each sandwich.
Sprinkle grated parmesan cheese over each sandwich before closing them up. Serve immediately.