In a bowl, season the ground beef with salt and pepper. Form into 4 equal patties.

Melt 1 tablespoon of butter in a skillet over medium heat. Add the sliced onions and cook until caramelized, about 10 minutes, stirring occasionally.

In the same skillet after the onions are done, increase the heat to medium-high and add the beef patties.

Cook each patty for about 3-4 minutes on one side, then flip and place a slice of cheddar cheese on each patty. Cook for another 3-4 minutes until the cheese melts and the patties are cooked to your liking.

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

In a clean skillet, place two slices of bread butter-side down. Top each with a patty and some caramelized onions, then cover with another slice of bread, butter-side up.

Grill the sandwiches for about 3-4 minutes on each side, or until golden brown and crispy.

Remove the patty melts from the skillet and let them rest for a minute before slicing in half.

Serve hot with your choice of condiments and sides.