Heat a griddle or skillet over medium heat and melt the butter on it.
Place 4 slices of sourdough bread on the griddle. Toast one side until golden brown, then flip them over.
On the toasted side of each bread slice, layer cheddar cheese, a bit of Italian pepper spread, coppa or prosciutto slices, and top with mozzarella cheese. Place the remaining 4 slices of bread on top of each sandwich with the toasted side facing down.
Cook the sandwiches for 3-4 minutes on each side until golden brown and the cheese is melted. Optionally, cover the sandwiches with a dome or lid while cooking to help melt the cheese evenly.
In the last few minutes of cooking, sprinkle shredded parmesan cheese onto the griddle in a shape similar to the bread slices. Top the parmesan with a few slices of jalapeno pepper, then place each sandwich directly on top of the parmesan and jalapenos.
Cook for an additional 2-3 minutes until the parmesan forms a crispy crust and the jalapenos soften slightly.
