Heat 1 tbsp of butter in a skillet over medium heat and add the sliced onions. Cook until caramelized, about 10 minutes.
In a bowl, mix ground beef with Worcestershire sauce, salt, and black pepper. Form into two patties.
In the same skillet, cook the patties for about 4-5 minutes per side until browned and cooked through.
Remove the patties and wipe the skillet clean.
Assemble the sandwich: Place a slice of cheese on a slice of rye bread, followed by a beef patty, caramelized onions, another slice of cheese, and top with another slice of rye bread.
Spread butter on the outside of the bread and grill the sandwich on medium-low heat until golden brown and crispy, about 3 minutes per side.
Serve hot and enjoy!
Notes
For extra flavor, try adding a special sauce made from mayonnaise, ketchup, and mustard.