- Heat 2 tablespoons butter in a skillet over medium heat. Add onions and sauté until translucent and lightly golden. Remove from pan and set aside. 
- Form ground beef into a patty sized to fit the rye bread slices. Season with salt and pepper. 
- Cook the patty in the same skillet to desired doneness. Remove and set aside. 
- Butter one side of each bread slice with remaining butter. 
- Place one slice of bread butter-side down on hot griddle or skillet. 
- Layer one slice of cheese, caramelized onions, cooked patty, and second slice of cheese on top. 
- Top with second bread slice, butter-side facing out. 
- Grill until bread is golden and crispy but not burned, approximately 3-4 minutes. 
- Carefully flip and grill the other side until golden and cheese is fully melted, another 3-4 minutes. 
- Remove from heat and slice diagonally before serving.