In a large skillet, cook steaks in 1 tablespoon oil over medium heat until no longer pink. Sprinkle with the oregano, salt and pepper. Top each with a slice of cheese; cover and cook for 1 minute or until melted.
Remove and keep warm. Drain drippings. In the same skillet, saute the onion, garlic and pepper rings in remaining oil until tender. Spoon over steaks.