In a small bowl, mix together the mayonnaise, ketchup, mustard, sweet pickle relish, smoked paprika, garlic powder, salt, and pepper. Stir until smooth, then set aside in the refrigerator.

Heat 2 tbsp of butter in a large skillet over medium heat. Add the sliced onions and cook, stirring occasionally, for about 15-20 minutes or until they are soft, golden brown, and caramelized. Remove from heat and set aside.

In a large bowl, combine the ground beef, diced onion, Worcestershire sauce, salt, and pepper. Mix gently, being careful not to overwork the meat. Divide into 4 equal portions and shape each into a patty about 1/2 inch thick.

Heat 1 tbsp of olive oil in the skillet over medium-high heat. Cook the patties for about 3-4 minutes per side, or until they are fully cooked through and nicely browned. Remove from heat and set aside.

Spread 1 tbsp of butter on one side of each slice of rye bread. On the unbuttered side, layer a slice of Swiss cheese, a beef patty, caramelized onions, a drizzle of secret sauce, and another slice of cheese. Top with another slice of rye bread, buttered side facing out.

Heat a skillet or griddle over medium heat. Place the sandwiches on the skillet and cook for 2-3 minutes on each side, pressing down lightly with a spatula, until the bread is golden and crispy and the cheese is fully melted.

Slice each patty melt in half and serve hot with extra secret sauce on the side for dipping.