In a large skillet, heat 2 tablespoons butter and oil over medium-high heat; cook steaks to desired doneness (for medium-rare, a thermometer should read 135°; medium, 140°), 5-6 minutes per side. Remove from pan, reserving drippings; keep warm., In same pan, heat drippings and remaining butter over medium-high heat; saute mushrooms and green onion until tender. Stir in flour, salt and pepper until blended; gradually stir in broth and, if desired, browning sauce. Bring to a boil, stirring constantly; cook and stir until thickened, 1-2 minutes. Serve with steaks.