Heat oven to 350 F. Heat oil in skillet over high heat. Season steaks with 1/4 teaspoon each of the salt and pepper. Add steak; sear to brown one side, 2 minutes. Turn; brown other side, 2 minutes.
Remove to shallow roasting pan; place in oven. Roast until desired doneness, 7 minutes for rare.
Lower heat to medium-high; add onions to same skillet. Cook, stirring, over high heat 4 minutes. Add garlic and remaining salt and pepper; cook 1 minute. Add mushrooms; cook, stirring, 3 minutes. Add wine; heat to boil. Cook, stirring up bits on bottom of skillet, to reduce, 5 minutes. Stir in butter.
Remove steaks from the over, plate, and spoon mushrooms and sauce over steaks.