Preheat broiler. Coat a large nonstick skillet with cooking spray; heat skillet over medium heat. Add mushrooms, onion, and garlic; cook for 5 to 10 minutes or until tender, stirring occasionally. Stir in tomato sauce, balsamic vinegar, rosemary, and dried oregano. Bring to boiling; reduce heat. Simmer, covered, for 2 minutes. Stir in meatballs. Simmer, covered, about 5 minutes more or until meatballs are heated through.
Meanwhile, open buns so they lay flat and place on a baking sheet. Broil 4 to 5 inches from the heat about 1 minute or until lightly toasted. Remove tops of buns from baking sheet. Divide meatball mixture among bottoms of buns; sprinkle with cheese. Broil for 1 to 2 minutes more or until cheese is melted. If desired, sprinkle with fresh oregano. Replace tops of buns.