Sprinkle steak with 1/4 teaspoon each salt and pepper. In a skillet, heat oil over medium-high heat; cook steak to desired doneness (for medium-rare, a thermometer should read 135°; medium, 140°), 4-6 minutes per side. Remove from pan; keep warm.
In same skillet, heat butter over medium-high heat; saute mushrooms until tender. Stir in wine; bring to a boil, stirring to loosen browned bits from pan. Stir in green onions, Worcestershire sauce, mustard and the remaining salt and pepper. Cut steak in half; serve with mushroom mixture.