In a large bowl, combine the beef, egg white, onion, crumbs, milk, horseradish, salt if desired, and pepper. Shape into four oval patties.
In a large skillet cook patties over medium heat for 5-6 minutes on each side or until a thermometer reads 160° and meat is no longer pink. Remove patties and keep warm. Add gravy, mushrooms and water to skillet; heat for 3-5 minutes. Serve over patties and noodles if desired.