1) Heat 1 tablespoon of the oil in a large cast-iron skillet over medium heat. Add the onions, and cook until golden brown and caramelised, about 15 minutes.
2) When caramelised add Worcestershire and season with salt and pepper, to taste. Put in a bowl.
3) Divide the meat into 4 portions, and then press each one into an oval patty about the size of the slices of bread.
4) Wipe out the skillet and add another tablespoon of oil. Season the patties with salt and pepper and cook over medium-high heat in batches if needed until well browned, about 1 to 2 minutes per side for medium-rare burgers.
6) Lay the bread on the counter. Divide the onions among 4 bread slices and top with a slice of cheese, a patty, another slice of cheese, and a slice of bread.
7) Heat the remaining olive oil in a cast-iron skillet over medium heat. Cook the sandwiches, in batches if needed, turning once, until the bread is lightly browned and the cheese has melted, 1 to 2 minutes per side. Halve the melts and serve.