In a large bowl, combine beef, Worcestershire sauce, garlic powder, salt, pepper and liquid smoke if desired, mixing lightly but thoroughly. Shape into four 4-in. square patties.
In a large nonstick skillet, cook burgers in oil over medium heat until a thermometer reads 160°, 4-5 minutes on each side. Remove and keep warm.
In the same skillet, heat 1 tablespoon butter over medium-high heat. Add onion; cook and stir until tender, 6-8 minutes. Remove and keep warm. Place cheese on 8 bread slices; top with remaining bread. Spread outsides of sandwiches with remaining 4 tablespoons butter.
In the same skillet, toast sandwiches over medium heat until golden brown and cheese is melted, 1-2 minutes on each side. Top 4 sandwiches with burgers and onions. Top with remaining sandwiches.
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