Meatballs: In a large bowl combine ground beef with salt, pepper, steak sauce, crumbs and egg, mixing gently until well blended. Shape mixture into large 1 1/2 to 2-inch meatballs. Brown meatballs in a large skillet in the butter. Reduce heat and continue cooking for about 10 minutes. Remove meatballs and set aside. Pour off all but about a tablespoon of the drippings.
Sauce: Add 1 tablespoon butter to the skillet, saute mushrooms and remove from heat. Stir in flour and ketchup; add broth gradually. Add onion soup mix, bring to a boil, then reduce heat and add meatballs. Stir in sour cream; heat through but do not boil. Serve with hot buttered noodles, mashed potatoes, or rice.