Grate 2 tablespoons onion; place in a large bowl. Chop remaining onion to measure 2 cups; set aside. Place bread in a food processor; pulse 10 times or until coarse crumbs measure 1/3 cup. Add the breadcrumbs, meat, 1/4 teaspoon pepper, and egg white to grated onion in bowl; mix with hands until well blended. Shape mixture into 42 (1-inch) meatballs; set aside.
Heat oil in a large Dutch oven over medium heat. Add 2 cups chopped onion and carrot; sauté 5 minutes or until vegetables are tender. Add water, consommé, and tomatoes; bring to a boil. Reduce heat to medium. Carefully add meatballs to soup; simmer 20 minutes or until meatballs are no longer pink. Stir in remaining 1/4 teaspoon pepper and spinach. Ladle soup into bowls, and sprinkle with Parmesan cheese.