Preheat your oven to 350°F. Slice the Hawaiian rolls horizontally to separate the tops and bottoms, then place the bottom layer inside your baking dish.
Lay provolone slices evenly over the bottom rolls. Add the ham, salami, and pepperoni in layers so each slider gets a good balance of meat and cheese.
Place the tops of the rolls back on. Mix the melted butter, Parmesan, garlic powder, and salt, then brush this mixture over the top. Bake for 15–20 minutes, or until the tops are golden and the cheese has fully melted.
While the sliders bake, whisk together the mayonnaise, red wine vinegar, Italian seasoning, salt, pepper, and garlic powder. Add the shredded lettuce, tomato, and pepperoncini, and toss until well coated.
Once the sliders are hot and golden, remove them from the oven. Lift the tops, spread the grinder salad evenly over the meat, and replace the tops. Slice and serve warm.