In a large saucepan or Dutch oven, saute celery, green peppers, onion and garlic in oil until tender, about 4-5 minutes. Add the next eight ingredients; bring to a boil. Reduce heat; simmer, uncovered, for 1-2 hours.
For meatballs, beat eggs in a large bowl. Add the next six ingredients. Crumble beef over mixture and mix well. Shape into 1-in. balls. Place meatballs on a greased rack in a shallow baking pan. Bake, uncovered, at 450° for 12-15 minutes or until no longer pink. Drain on paper towels. Add to sauce; heat through. Serve on buns; top with Parmesan cheese if desired.