Heat a skillet over medium heat and melt 1 tablespoon of butter.
Add sliced onions and cook until caramelized, about 5-7 minutes.
Season the ground beef with salt and pepper and form into two patties.
Increase skillet heat to medium-high and add the patties.
Cook patties for 3-4 minutes on each side, adding cheese during the last minute.
Spread butter on one side of each slice of bread.
Assemble the sandwich by placing the patty with cheese between two slices of bread.
Grill the sandwich until both sides are golden brown.
Remove from heat and let cool slightly before slicing.
Serve warm and enjoy!