Mix ground beef, bread crumbs, salt, pepper and egg; shape into 4 oval patties, each about 3/4-inch thick.
Cook patties in 10-inch skillet over medium heat, turning occasionally, until brown, about 10 minutes.
Add onion, broth and mushrooms. Heat to boiling; reduce heat. Cover and simmer until beef is done, about 10 minutes. (I usually start boiling the water for homemade mashed potatoes at this time and the steaks will be ready by the time you get the mashed potatoes ready).
When patties are done, remove them from skillet. Keep warm.
Heat onion mixture to boiling. Mix water and cornstarch; stir into onion mixture. Boil and stir 1 minute.