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.