In a large saucepan or Dutch oven, saute celery, green peppers, onion and garlic in oil until tender, 4-5 minutes. Add the next 8 ingredients; bring to a boil. Reduce heat; simmer, uncovered, for 1-2 hours.
For meatballs, beat eggs in a large bowl. Add the next 6 ingredients. Crumble beef over mixture and mix lightly but thoroughly. Shape into 1-in. balls. Place meatballs on a greased rack in a shallow baking pan. Bake, uncovered, at 450° until no longer pink, 12-15 minutes. Drain on paper towels. Add to sauce; heat through. Serve on buns; top with Parmesan cheese if desired.