In a large bowl, mix together 1/3 cup condensed french onion soup with ground beef, bread crumbs, egg, salt and black pepper. Shape into 6 oval patties.
In a large skillet over medium-high heat, brown both sides of patties. Pour off excess fat. Remove patties from the pan and add sliced onions and peppers and saute until softened. Add patties back to pan.
In a small bowl, blend flour and remaining soup until smooth. Mix in ketchup, water, worcestershire sauce and dry mustard. Pour over meat, onions and peppers in the skillet. Cover and cook for 20 minutes, stirring occasionally.