Make the meatballs: Preheat the broiler. In a large mixing bowl, whisk together the eggs, pecorino, parsley, garlic and some salt and pepper until it is all incorporated. Add the ground meats and breadcrumbs and, using your God-given hands, get after it and mix away. Do not overwork the meat or it will turn meatloaf-y. You want it loose and supple.
Using your hands again, make 6 loose patties to match the size of your bread. Heat some oil in a large heavy-bottomed cast-iron pan (or use a griddle pan) over medium heat. In batches, fry the patties until golden brown, 4 to 5 minutes per side. Transfer to a baking sheet.
For the sandwich build: Toast the split buns under the broiler, about 3 minutes. Spoon 3 tablespoons of sauce on top of each patty and top with a few slices of mozzarella. Place the patties under the broiler until melted and golden, 3 to 5 minutes. Place the patties on the buns and top with giardiniera and roasted red peppers. Cut in half and serve with the remaining marinara sauce on the side.