Season the ground beef generously with salt and pepper. Divide into three equal portions and shape each into a thin patty, pressing an indentation in the center to prevent puffing.

In a skillet over medium heat, add a pat of butter and the sliced onions. Cook, stirring occasionally, until golden and tender (about 8–10 minutes). Transfer onions to a bowl.

In the same skillet, sear each patty over medium-high heat for 3–4 minutes per side, or until cooked through. Remove and set aside.

Spread butter on one side of each rye slice. Turn buttered side out and layer: bread, cheese, beef patty, caramelized onions, another slice of cheese, and top with bread.

Heat the skillet over medium-low. Place sandwiches in the pan, pressing down gently. Cook 3–4 minutes per side until the bread is crispy and cheese is melted.

Let sandwiches rest 1 minute. Slice in half and serve hot with pickles or fries.