Melt butter in a skillet over medium heat. Add sliced onions and stir gently. Let them cook down for about 15-20 minutes until they're beautifully caramelized and fragrant, stirring occasionally to avoid burning.

Season the ground beef with salt and pepper. In a bowl, mix well before forming the seasoned beef into two equal-sized patties, ready to unleash their juicy goodness.

Cook the patties in a separate skillet over medium-high heat. Cook each side for about 4-5 minutes until they develop a rich brown crust.

Top each patty with a slice of Swiss cheese during the last minute of cooking. Cover the skillet to help the cheese melt.

Assemble your sandwich: Place a cheesy patty on one slice of rye bread, generously pile on the caramelized onions, and finish with another slice of bread.

Grill the assembled sandwich in a clean skillet, pressing down gently, until both sides are golden brown and crispy, and the cheese is perfectly melted.