1. In a small bowl, whisk together the mayonnaise, ketchup, Dijon mustard, dill pickle juice or chopped dill pickles, garlic powder, smoked paprika, salt, and pepper until smooth. Taste and adjust seasoning as needed, then refrigerate the secret sauce while you prepare the rest of the recipe.

2. Melt the 2 tablespoons butter in a large skillet over medium heat. Add the sliced onions and a small pinch of salt. Cook, stirring every few minutes, until the onions are soft, golden, and deeply caramelized, 15 to 20 minutes. If they start to brown too quickly, lower the heat and add a teaspoon of water as needed. Transfer the onions to a bowl and set aside.

3. In a mixing bowl, gently combine the ground beef, Worcestershire sauce, salt, and pepper just until everything is evenly distributed. Divide the mixture into 4 equal portions and shape each into a thin patty slightly larger than your bread slices.

4. Return the skillet to medium high heat and add a drizzle of neutral oil if the pan looks dry. Cook the patties 3 to 4 minutes per side, or until nicely browned on the outside and cooked through to your liking. Transfer the cooked patties to a plate and wipe out the skillet if there are any burned bits.

5. Spread one side of each bread slice with softened butter. Lay 4 slices, buttered side down, on a board or tray. Spread each with a spoonful of secret sauce, then top with 1 slice of cheese, 1 warm beef patty, a generous spoonful of caramelized onions, and a second slice of cheese. Spread the remaining 4 bread slices with more secret sauce and place them on top, sauce side down, so the buttered sides face outward.

6. Heat the skillet or a griddle over medium heat. Place the sandwiches in the pan, working in batches if needed. Cook 3 to 4 minutes per side, pressing lightly with a spatula, until the bread is deeply golden and crisp and the cheese inside is fully melted. Adjust the heat so the bread browns without burning while the cheese melts.

7. Move the cooked patty melts to a cutting board and rest for 1 to 2 minutes. Slice each sandwich in half diagonally and serve immediately with any remaining secret sauce on the side for dipping.