In a bowl, combine the egg, bread crumbs, 1/4 cup soup and onion. Crumble the beef over mixture and mix well. Shape into eight patties. In a large non-stick skillet, brown the patties on both sides; drain.
In a 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 meat is no longer pink.