In a large bowl, combine the egg, bread crumbs, 1/4 cup soup and onion. Crumble the beef over mixture and mix well. Shape into six patties. In a large nonstick skillet, brown the patties on both sides; drain.
In a small bowl, combine the milk, browning sauce if desired, salt and remaining soup; stir in mushrooms.
Pour over patties. Reduce heat; cover and simmer for 15-20 minutes or until a meat thermometer reads 160° and meat is no longer pink.