Instructions:

1. Prepare the Beef Patties: In a bowl, combine the ground beef, Worcestershire sauce, salt, and black pepper. Form the mixture into two equal-sized patties.

2. Cook the Onions: In a skillet over medium heat, melt 2 tablespoons of butter. Add the sliced onions and sauté until they are caramelized and golden brown, about 10-15 minutes. Stir occasionally to prevent burning. Once done, remove from the skillet and set aside.

3. Cook the Patties: In the same skillet, add the beef patties. Cook for about 4-5 minutes on each side, or until they reach your desired doneness. If using Swiss cheese, place a slice on each patty during the last minute of cooking to allow it to melt.

4. Assemble the Patty Melt: On a slice of rye bread, place a patty with melted cheese, followed by a generous portion of the caramelized onions. Top with another slice of rye bread.

5. Grill the Sandwich: Wipe the skillet clean and add 2 tablespoons of butter. Place the assembled sandwiches in the skillet and grill over medium heat until the bread is golden brown and crispy, about 3-4 minutes on each side.

6. Serve: Remove from the skillet, slice in half if desired, and serve hot with your favorite sides, like fries or a salad.