1. In a skillet, melt 1 tablespoon of butter over medium heat. Add sliced onions and cook until caramelized, about 10 minutes. Remove from skillet and set aside.
2. In a mixing bowl, combine ground beef with salt and pepper. Form into 4 patties.
3. In the same skillet, cook patties over medium-high heat until browned and cooked through, about 4 minutes per side. Remove from skillet.
4. To make the special sauce, mix mayonnaise, ketchup, Dijon mustard, Worcestershire sauce, and garlic powder in a bowl.
5. Spread butter on one side of each slice of rye bread. On the unbuttered side, spread special sauce, then add a slice of Swiss cheese, a patty, caramelized onions, and another slice of Swiss cheese. Top with another slice of bread, buttered side out.
6. In the skillet, cook the sandwiches over medium heat until the bread is golden brown and the cheese is melted, about 3 minutes per side.