In a medium bowl, whisk together mayonnaise, red wine vinegar, olive oil, oregano, garlic powder, salt, and black pepper until smooth.
Add the shredded lettuce, sliced red onion, and banana peppers to the bowl. Toss until lightly coated. Set aside.
Slice the rolls open. Place provolone on the bottom halves and toast in the oven or air fryer for about 2 minutes, just until the cheese starts to melt and the bread is lightly crisp.
Layer the salami, pepperoni, and ham (or mortadella) over the melted cheese, folding slices slightly for a deli-style look and bite.
Spoon the grinder slaw over the meat. If not using the slaw method, layer lettuce, tomato, onion, and peppers, then drizzle the dressing on top.