Divide beef into 4 equal portions, shaping each into a 1/2 inch-thick patty. Sprinkle patties evenly with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Heat 2 teaspoons oil in a large skillet over medium-high heat; swirl to coat. Add the patties; cook 3 minutes on each side or until browned; remove from the pan.
Add the remaining 1 teaspoon oil to the pan; swirl to coat. Add vertically sliced onion, saute 3 minutes or until lightly browned and tender. Sprinkle onion with flour; cook 3 sweconds, stirring constantly. Add the stock and sherry and the remaining salt and pepper; bring to a boil.
Return the patties to the pan; reduce heat to medium, partially cover, and cook 5 minutes or until the gravy is slightly thickened. Sprinkle with green onions if desired.