Prep Naan: Lay naan breads on a pan. Pour Italian dressing into a small bowl. Brush some dressing over the naan with a pastry brush (save some dressing for later).
Add Cheese and Meat: Sprinkle provolone and Parmesan cheese evenly over both naan breads. Then, sprinkle the chopped salami, pepperoni, and turkey.
Preheat Grill: Heat your grill to about 400°F (or use a flattop).
Make Salad: In a bowl, combine lettuce, red onion, banana peppers, and grape tomatoes. Toss with the remaining Italian dressing.
Grill Naan: Place naan on the grill for about 3 minutes until cheese melts and the bottom is crispy.
Top and Serve: Remove from grill, top with the salad mix, slice, and serve.