Heat the olive oil in a large skillet over medium high heat. Add the onions and cook for 20 minutes, until they have caramelized. Remove the onions from the skillet and set aside.
Heat the olive oil in a large skillet over medium high heat. Add the beef patties to the hot skillet and season with salt and pepper.
Cook on each side for 2 minutes, or until beef is cooked through. Remove the patties from the skillet and wipe the pan if needed.
Butter each slice of bread on one side. Place one slice of bread butter side down in the hot skillet. Add 1 beef patty to the top of the bread slice along with ¼ of the onions and a slice of cheese.
Top each sandwich with the 2nd slice of bread. Cook for 3-4 minutes or until the bread is toasted. Flip the sandwich over and cook 3 minutes more, until bread is toasted and the cheese has melted.