In a large pot, saute onion, garlic, carrots, and celery in 2 tablespoons butter or margarine until soft, about 5 to 6 minutes. Stir in broth,tomato sauce, and beef. Simmer covered for 15 to 20 minutes, or until vegetables are tender. Season to taste with salt and pepper.
In a bowl, mix 2 tablespoons butter or margarine, eggs, flour, and salt until smooth. Drop mixture into soup by small teaspoonfuls. Cover, and simmer for 10 minutes.