Heat oil in a skillet on medium heat.
Add onions, cook until deeply golden (15 minutes).
Season onions with salt, then remove from skillet.
Form ground beef into four oval patties.
Season both sides with salt and pepper.
Cook patties in skillet, 3-4 minutes per side.
Remove patties and wipe skillet clean.
Butter one side of each bread slice evenly.
Layer sandwich: bread, cheese, patty, onions, cheese.
Top with another slice, buttered side out.
Cook sandwich on medium heat until golden brown.
Flip gently and toast the other side.
Cook until cheese is fully melted.
Slice and serve warm for best flavor.