In a large mixing bowl combine ground beef, egg, ¼ cup of the soup, bread crumbs, 1 Tablespoon onion soup mix and pepper and shape into 6 patties.
Heat a nonstick skillet over medium heat and brown the patties, turning once.
Meanwhile, in a bowl combine the remaining soup, water, ketchup, remaining 2 Tablespoons onion soup mix, flour and Worcestershire sauce, stirring until blended.
Add the sauce mixture to the skillet and bring to a boil.
Spoon some of the sauce over the patties.
Reduce the heat to medium-low and cook, covered, until the beef is cooked through, about 20 minutes, occasionally spooning gravy over the patties. Check the temperature of the beef patties with an instant read thermometer. Patties should cook until they are at 160F.