Put half of the butter into a skillet over medium high heat. Once melted, add onions and sprinkle with salt and pepper. Lower heat to medium low, stirring the onions frequently. Continue to sauté for 30 - 40 minutes until caramelized. Remove from heat and set aside.
While your onions are caramelizing, in a medium sized bowl add the ground beef and generously season with salt and pepper. Add Worcestershire sauce, onion powder, and garlic powder. Mix well with your hands. Separate and roll into 4 even balls.
Place plastic wrap on a cutting board and add a patty. Place another piece of plastic wrap on top and use a plate or other flat surface to evenly flatten the patty. Shape into an oval shape to match the bread size.
Slather one side of the Rye bread slices with mayo and the other with butter.
Heat your skillet to medium and carefully place your patties. Sear on each side for 3 minutes. On the second side, add some of the onions and top with a slice of Swiss. Cover with a lid or baking sheet for a minute to melt the cheese. Remove from the skillet.
Add 2 - 4 slices of bread to the skillet butter side down (as many as will fit in your skillet). Add patties and top with other piece of bread. Toast until golden brown, about 2 - 3 minutes. Then flip and cover for another minute or two.
Remove and place on a cutting board. Slice down the middle and enjoy.