Heat the oil in heavy large frying pan over medium-high heat. Working in 2 to 3 batches, add the meatballs and saute until browned on all sides, about 5 minutes. Using a slotted spoon, transfer the meatballs to a plate. Pour off any excess oil. Return all the meatballs to the pan. Add the marinara sauce. Simmer over medium-low until the sauce thickens slightly and the flavors blend, about 10 minutes. Season the sauce, to taste, with salt and pepper. (The meatball mixture can be made 1 day ahead. Cool, then cover and refrigerate. Rewarm over medium heat before continuing.)
To make the sandwiches: Spoon the hot meatballs with some sauce over the bottoms of the rolls. Place 1/2 slice provolone on top of meatballs and sprinkle with the Parmesan. Spread more sauce over the roll tops, then fold the tops of the rolls over and serve.
Cook's Note: The sandwiches can be assembled then wrapped individually in foil. Rewarm the sandwiches in the oven at 350 degrees F for about 15 minutes.
Yield: 2 quarts
Prep Time: 10 minutes
Cook Time: 1 hour 10 minutes