In a skillet, melt 2 tablespoons of butter over medium heat and add sliced onions. Cook, stirring occasionally until onions are tender, but not mushy. Remove from skillet and keep warm.
Use remaining softened butter, butter one side of each slice of bread and set aside.
Form ground beef into 2 patties slightly larger than a bread slice.
Heat skillet to medium-high heat and cook meat patties until desired doneness is reached. Set aside.
Work quickly so the meat does not get cold, wipe out the skillet and place back on medium-heat.
Add 2 slices of bread to skillet with buttered side down.
Place a meat patty on top of each slice of bread.
Top each meat patty with 2 slices of Swiss cheese.
Top each with half of the onions and the last slices of bread, butter side up.
Leave in skillet until bread is lightly toasted.
Carefully flip sandwich and toast the other side.
Remove from skillet.