Prepare the secret sauce: Combine mayonnaise, ketchup, sweet pickle relish, and Worcestershire sauce in a small bowl. Mix well and set aside.
Caramelize the onions: Heat 1 tablespoon of butter in a large skillet over medium heat. Add the sliced onions and cook, stirring occasionally, until they are caramelized (about 15-20 minutes). Remove from the skillet and set aside.
Cook the patties: Divide the ground beef into 4 equal portions and shape them into thin patties. Season with salt and pepper. Cook in the same skillet over medium-high heat until cooked through (about 3-4 minutes per side). Remove from the skillet and set aside.
Assemble the patty melts: Butter one side of each slice of rye bread. Place 4 slices, butter-side down, on a clean skillet or griddle over medium heat. Top with a slice of Swiss cheese, a cooked patty, caramelized onions, a slice of cheddar cheese, and another slice of bread, butter-side up.
Cook and serve: Cook until the bread is golden brown and the cheese is melted (about 2-3 minutes per side). Remove from the skillet and let rest for a minute before slicing in half. Serve immediately with the secret sauce on the side or drizzled over the top.
