Sauté onions in 1 Tablespoon butter in a large non-stick skillet over medium heat until nicely browned, about 20 minutes. Season to taste with salt and pepper. Remove onions to a bowl; keep warm.
Melt remaining 1 Tablespoon butter in the same skillet in which the onions were cooked over medium high heat. Add liver and cook just until cooked through, about 2 minutes per side (the liver is done when no more blood forms on the top). Transfer liver to warmed plates; divide onion mixture evenly between the two pieces of liver. Serve immediately. Serve with baked potato, a steamed medley of fresh vegetables and red wine. Yield: 2 servings.