Caramelize the Onions
Heat a skillet over medium-low heat. Add butter and sliced onions. Cook slowly for 20–30 minutes, stirring occasionally, until soft and deeply golden. Remove and set aside.
Cook the Beef Patties
Shape ground beef into thin patties slightly larger than the bread. Season with salt and pepper. Cook in a hot skillet until browned on both sides and cooked through. Remove and rest briefly.
Assemble the Sandwiches
Butter one side of each bread slice. Place one slice butter-side down in the skillet. Add cheese, a beef patty, caramelized onions, another slice of cheese, then top with another slice of bread (butter-side up).
Grill Until Golden
Cook over medium heat until the bread is golden and crisp and the cheese melts. Flip carefully and repeat on the other side.
Serve
Slice in half and serve immediately while hot and melty.