Sprinkle salt and pepper over steaks. Heat oil in a 9-inch cast-iron skillet over medium-high heat until hot. Add steaks; cook 5 minutes on each side or until desired degree of doneness. Remove steaks from skillet; keep warm. Add shallots to skillet; sauté 30 seconds. Add cognac; cook 10 seconds. Add broth and mustard; stir well. Reduce heat; cook 2 minutes, stirring constantly. Serve steaks with sauce.
My husband and I love this so much, it is our "go-to" filet mignon.