Trim fat from steaks. Spread mustard evenly over both sides of steaks. In a large skillet heat 1 tablespoon of the oil over medium-high heat. Add steaks; reduce heat to medium. Cook to desired doneness, turning once. Allow 7 to 9 minutes for medium-rare (145 degrees F) to medium (160 degrees F). Transfer steaks to a serving platter; keep warm.
Add remaining 1 tablespoon oil to drippings in skillet. Add mushrooms; cook and stir for 4 minutes. Stir in wine, Worcestershire sauce, and thyme. Simmer, uncovered, for 3 minutes. Spoon over steaks.