Shape the patties: Start by shaping the ground beef into four oval patties, lightly seasoning each with salt and pepper.
Cook the patties: On a medium-high heat skillet, cook the patties for about 4 minutes on each side or until your preferred doneness is reached. Set them aside on a plate.
Caramelize the onions: In the same skillet, lower the heat to medium and add a little butter if needed. Toss in the sliced onions and cook, stirring occasionally, until they become caramelized and sweet – this could take around 10 minutes.
Prepare the bread: While the onions are caramelizing, butter one side of each slice of rye bread. These will be the outsides of your sandwiches—toasted to a golden-brown.
Assemble the sandwich: Transfer the onions to a dish, then wipe the skillet clean with a paper towel. Place a slice of bread, butter-side down, followed by a slice of Swiss cheese, a portion of caramelized onions, a beef patty, another slice of cheese, and top it with a second slice of bread, butter-side up.
Cook the sandwich: Cook the assembled sandwich on medium heat for about 3 minutes per side, or until the bread is toasty and the cheese has begun to melt lovingly around the edges.
Serve: Serve warm, perhaps halved to reveal the layers of melted goodness. Offer Thousand Island dressing for dipping or drizzling if desired.