In a mixing bowl, combine the ground beef, garlic powder, onion powder, salt, and pepper. Mix until just combined, then form into two equal patties.

Heat a skillet over medium heat and add 1 tablespoon of butter. Once melted, add the sliced onions and cook until caramelized, about 10-15 minutes, stirring occasionally. Remove the onions from the skillet and set aside.

In the same skillet, add the remaining tablespoon of butter. Cook the beef patties for about 4-5 minutes on each side, or until they reach your desired doneness. In the last minute of cooking, add Worcestershire sauce to the patties.

Place a slice of cheese on each patty and cover the skillet to melt the cheese, about 1-2 minutes.

Assemble the patty melt by placing a patty with melted cheese on a slice of rye bread, topping it with caramelized onions, and then placing another slice of rye bread on top.

Grill the sandwich in the skillet for 2-3 minutes on each side, or until the bread is golden brown and crispy.

Slice in half and serve hot.