Place bread in medium bowl; cover with milk. Let stand until bread is soft, about 10 minutes. Place meat in large bowl. Mix in 2 tablespoons cheese and next 5 ingredients. Squeeze bread almost dry; discard milk. Blend bread into meat mixture. Using 1 rounded tablespoon for each, shape mixture into 24 meatballs.
Heat oil in heavy large skillet over medium heat. Add meatballs; sauté until brown and cooked through, turning often to hold shape, about 15 minutes. Add meatballs and drippings in skillet to pot of Tomato-Sausage Sauce. Simmer to blend flavors, about 10 minutes.
Place pasta in large bowl. Add 1 1/2 cups sauce and toss to coat. Top with meatballs and remaining sauce. Serve with additional Parmesan cheese.