Begin by preheating your oven to 350 degrees Fahrenheit (175 degrees Celsius).
Unroll one package of the crescent roll dough and evenly distribute it across the bottom of a 9x13 inch baking pan. On top of this dough layer, arrange the ham, provolone cheese, Swiss cheese, salami, pepperoni, and roasted red peppers.
In a separate bowl, lightly beat the eggs, then combine them with the grated Parmesan cheese and ground black pepper. Pour three-quarters of this egg mixture over the layered peppers. Unroll the second package of dough and place it atop the peppers, brushing it with the remaining egg mixture. Cover the pan with aluminum foil.
Bake in the preheated oven for 25 minutes. After this time, remove the foil and continue baking until the dough is fluffy and turns a golden brown color, which should take an additional 10 to 20 minutes. Once baked, cut into squares and serve warm or at room temperature.