Halve filet crosswise and season with salt and pepper. Heat oil over moderate heat in a small heavy skillet until hot but not smoking, then cook filets 2 to 3 minutes on each side for rare. Let stand on a cutting board, tented loosely with foil, 5 minutes. While filets are standing, deglaze skillet with Cognac over moderate heat, scraping up brown bits. Add broth and water and boil until reduced to about 1/4 cup. Remove from heat and whisk in mustard, butter, any meat juices from cutting board, and salt and pepper to taste. Thinly slice filets and serve with sauce.