Prepare the meatballs

In a large bowl, combine the bread crumbs and milk. Let stand for 5 minutes. In a frying pan over medium-high heat, warm the 1 tablespoon oil. Add the onion and garlic and sauté for about 5 minutes. Let cool slightly and add to the bread crumb mixture. Add the egg, parsley, 1 teaspoon salt, ¼ teaspoon pepper, and the beef and mix gently with your hands. Form into 12 equal-sized meatballs.

Cook the meatballs

In a large frying pan over medium heat, pour oil to a depth of ½ inch (12 mm). When the oil is hot, add the meatballs. Cook, turning, until browned on all sides, about 8 minutes. Transfer to paper towels to drain. Discard the oil and place the pan over medium-low heat. Add the tomato sauce and stir, scraping up any browned bits on the pan bottom. Add the meatballs and cook, covered, until heated through, about 10 minutes. Meanwhile, preheat the oven to 450°F(230°C). Place the rolls, cut sides up, on a rimmed baking sheet. Spread some of the sauce on the bottom half of each roll. Arrange 3 meatballs on each roll and top with the cheese. Bake until the cheese melts, about 5 minutes. Transfer to plates, top with the remaining sauce and roll tops, and serve.