Preheat the oven to 350°F and line a baking sheet with parchment paper.
Using a bread knife, slice the dinner rolls in half horizontally, keeping them connected, and place the bottom half on the baking sheet.
Layer the sliced ham, then salami, then pepperoni over the bottom buns.
Add a layer of provolone cheese and sprinkle with Italian seasoning.
Top with chopped tomatoes, red onions, and sliced pepperoncini peppers.
Place the top buns back on the sliders.
In a microwave-safe bowl, melt together butter, Dijon mustard, garlic powder, and Italian seasoning for about 10 seconds, then stir.
Brush the butter mixture evenly over the tops of the buns and sprinkle grated Parmesan cheese on top.
Cover the sliders with foil and bake for 15 to 20 minutes until the cheese melts and aroma develops.
Remove the foil and bake for an additional 5 minutes until the tops are toasted.
Remove sliders from the oven, lift the top buns, add shredded lettuce for crunch if desired, then replace the buns and serve warm.