5. Assemble the patty melts: Remove any excess grease from the skillet and melt 2 tablespoons of the remaining butter in a medium saucepan. Place four slices of rye bread in the pan, buttered side down. Top each bread slice with a burger patty, Swiss cheese, half of the caramelized onions, and another slice of cheese. Sandwich the melts together with the remaining four slices of buttered bread, buttered side up.
6. Cook the assembled melts for two to four minutes on each side, using a spatula to gently press down on the cheese occasionally, or until golden brown and melted.
7. Once the patty melts are cooked, transfer them to a cutting board and cut them diagonally. Enjoy!
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