In a small mixing bowl, combine mayonnaise, ketchup, Dijon mustard, sweet pickle relish, Worcestershire sauce, salt, and pepper. Mix well and set aside.

In a small saucepan over medium heat, melt 1 tablespoon of butter. Add the thinly sliced onions and cook, stirring occasionally, until they are soft and caramelized, about 15-20 minutes. Remove from heat and set aside.

In a mixing bowl, combine the ground beef, Worcestershire sauce, salt, and pepper. Mix until just combined. Divide the mixture into 4 equal portions and shape each portion into a patty.

Heat a skillet or griddle over medium-high heat. Cook the beef patties for about 3-4 minutes on each side, or until they reach your desired level of doneness. Remove from heat and set aside.

Butter one side of each slice of bread. Place a slice of bread, buttered side down, on the skillet or griddle. Layer with a slice of Swiss cheese, a beef patty, caramelized onions, a slice of cheddar cheese, and another slice of bread, buttered side up.

Cook the sandwiches over medium heat until the bread is golden brown and the cheese is melted, about 3-4 minutes per side. Use a spatula to press down gently on the sandwiches to ensure even toasting.

Cut the patty melts in half and serve immediately with a side of the secret sauce for dipping.