In a large mixing bowl, whisk together the eggs, Romano, parsley, garlic, and some salt and pepper until it is all incorporated.
Add in 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 "meat-loafy." You want it loose and supple.
Using your hands again, make 4 loose patties to match the size of your bread. (The mixture will form at least 10 patties, depending on how big your buns are. But I like to make some patties for sandwiches and then roll the rest to make meatballs, which I then freeze so I have meatballs at the ready.)
Heat some oil in a large 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.
For the sandwich build: Place the buns split-side up on a rimmed baking sheet. Add 1 slice of provolone to each side of the buns and broil in the oven until the cheese is brown and bubbly, 1 to 2 minutes, but keep watch!
Add the patties to the bottom buns, spoon over some marinara, top with some red pepper strips and pile on some giardiniera. Then close the sandwiches and eat the hell out of them.