Combine ground beef, chopped onion, bread crumbs, egg, salt, and black pepper in a bowl until evenly mixed. Shape beef mixture into four patties, about 3/4 inch thick.
In a large skillet fry patties over medium heat until browned on both sides, for about 10 minutes. Add beef broth, mushrooms and onion; bring to a boil. Reduce heat to low, cover, and simmer till patties are no longer pink in the center, for about 10 minutes more. Transfer patties to a platter and keep warm.
Bring onion mixture to a boil. In a small bowl mix cornstarch and water; stir into onion mixture. Cook and stir till onion gravy is thickened, about one minute. Pour over patties to serve.
