1. Combine turkey, bread crumbs, egg, Parmesan, salt and garlic powder in a large bowl. Mix gently with hands. Form into 1 dozen 2-inch balls.
2. Warm oil in a large nonstick pot over medium heat. Cook meatballs, turning occasionally, until brown on all sides, 6 to 8 minutes. Add sauce, bring to a simmer, reduce heat to medium-low and simmer until meatballs are cooked through, about 15 minutes.
3. Preheat broiler to high. Line a baking sheet with foil. Remove doughy centers from rolls and place 1 cheese slice in each. Broil until cheese melts, 1 to 2 minutes. Spoon meatballs and sauce into rolls and serve immediately.