Coat a large frying pan with oil. Set over medium-high heat. When hot, add steaks. For medium-rare,cook until well browned and meat gives slight resistance when pressed, 2 to 3 minutes per side.Remove to plates.
Reduce heat to medium. Add garlic butter to pan. When melted,add mushrooms. sprinkle with salt and pepper. Stir often until edges turn brown,3 to 4 minutes. Add chicken broth and sherry. Scrape bottom of pan to stir up any brown bits. Boil,stirring occasionally to develop flavour,2minutes. Spoon over steaks. Sprinkle with green onion.