Unroll one package of the crescent sheets and press into the bottom and up the sides of a 9x13-inch baking dish.
Layer on the salami, provolone, pepperoni, mozzarella, capicola, fontina, and roasted red peppers.
In a small bowl, whisk together 3 of the eggs with the Parmesan cheese and black pepper. Pour over the roasted red peppers.
Unroll the second package of crescent sheets and place over the filling.
In a small bowl, lightly beat the remaining egg and brush over the pastry.
Cover the pan with aluminum foil and bake for 30 minutes. Remove the foil and bake for an additional 20 to 30 minutes, until puffed and golden brown. Let stand for at least 30 minutes before slicing and serving. These can be served warm or at room temperature.
You can also use crescent rolls instead of the crescent sheets, but you will need to be sure to press together the perforations in the dough before using.