In a large bowl, combine the eggs, bread crumbs, cheese and pepper. Crumble beef, pork and veal over mixture and mix well. Shape into 1-1/2-in. balls.
Place meatballs on a greased rack in a shallow baking pan. Bake at 350° for 20-25 minutes or until no longer pink.
Place the meatballs, potatoes, carrots, celery, onion and garlic in a Dutch oven. In a small bowl, combine soup mix and water; pour over meatball mixture. Bring to a boil. Reduce heat; cover and simmer for 25-30 minutes or until vegetables are tender. Stir in peas and parsley; heat through.