Season the beef as desired. Cook the beef in a 12-inch nonstick skillet over medium-high heat to desired doneness, turning once during cooking. Remove the beef from the skillet. Cover and keep warm. Do not pour off any fat.
Heat the butter in the skillet. Add the mushrooms and cook until they're tender. Stir in the flour and cook for 1 minute. Gradually stir in the broth. Cook and stir until the mixture boils and thickens. Serve the mushroom gravy with the beef.