Heat a heavy grill pan or griddle pan over high heat. Wipe hot grill or griddle with extra-virgin olive oil. Cook steaks 6 minutes on each side for medium doneness, 8 minutes for medium well. Season steaks with steak seasoning or salt and pepper and remove to a warm platter to allow the meat to rest.
Heat a medium nonstick skillet over medium high heat. Add oil and onions and cook, stirring occasionally, 10 to 12 minutes, until onions are soft and sweet. Add balsamic vinegar to the pan and turn onions in vinegar until vinegar cooks away and glazes onions a deep brown color, 3 to 5 minutes.
Heat a small saucepan over medium heat. Add oil, garlic and onions and saute 5 minutes until onion bits are tender. Add sherry to the pan and combine with onions. Stir in tomato sauce and Worcestershire and season with black pepper.
To serve, top steaks with onions and drizzle a little steak sauce down over the top, reserving half of the sauce to pass at table.