Place the bottoms of the buns on a work surface, cut-side up. Top with the salami, fontina, and pepperoncini (if using). Sandwich with the tops of the buns. Flatten slightly with the back of a spatula.

Heat a large skillet over medium heat. Spread the top of each sandwich with 1/2 tablespoon of the butter or oil. Cook the sandwiches buttered-side down, pressing occasionally with the back of a spatula, for 2 minutes. Flip and cook until the cheese melts and the bread is golden.