Begin by shaping the ground beef into four thin patties, seasoning generously with salt and black pepper.

Melt 2 tablespoons of unsalted butter in a skillet over medium heat and cook thinly sliced onions for 15-20 minutes until caramelized.

Increase heat and cook beef patties for 3-4 minutes on each side until nicely browned.

Spread remaining butter on one side of each slice of rye bread.

Assemble the sandwich with buttered rye bread, Swiss cheese, beef patty, caramelized onions, and another slice of cheese, topped with bread.

Grill the sandwich in the skillet for 3 minutes on each side until golden and crispy.

Let the sandwich rest for a minute before cutting in half and serving warm.