Mix meat, onion, salt, Worcestershire sauce and pepper. Shape mixture into 6 patties, each about 3/4-inch thick. Brown patties in a large skillet over medium-high heat, turning once. Remove patties and set aside. Pour fat from the skillet. Mix water and seasoning mix in the same skillet and heat to boiling. Reduce the heat and return the patties to the skillet. Turn each one to coat with the sauce. Peel avocado and cut into 6 rings. Top each patty with an avocado ring. Cover and simmer 10 minutes. Sprinkle with the cheese; cover and heat until the cheese has melted, about 2 minutes. Serve sauce over the patties.
NOTE: You can substitute 1 medium tomato, sliced for the avocado rings.