Brown the ground beef in a medium skillet over medium-high heat, until meat is no longer pink. Add onion and mushrooms to mixture, saute.
Drain excess fat and set aside.
Melt the butter or margarine in a medium saucepan over medium heat. Slowly add the flour, stirring constantly, to form a brown roux.
Pour in beef broth and milk, mixing well. Add ground beef, then season with salt and pepper to taste. Serve this dish over toast or english muffins.