Combine mayonnaise, ketchup, dijon mustard, pickle juice, paprika, and garlic powder in a small bowl. Whisk until well emulsified and smooth. Reserve for sandwich assembly.

Warm olive oil in a skillet set over medium-low heat. Add the sliced onions and sauté slowly, stirring occasionally, until they reach a deep golden brown hue and are fully softened, about 30 minutes. If the onions begin to char or dry out, reduce heat and add a splash of water as needed. Set aside once cooked.

Place the ground beef in a mixing bowl and season with salt, pepper, and Worcestershire sauce. Gently blend until combined, then shape into four elongated patties, tailored to the shape of the bread slices. Heat a skillet over medium and sear the patties until browned on each side and cooked through. Remove and set aside. Wipe the pan to eliminate any excess fat.

Spread softened butter on one side of each bread slice. In the skillet over medium heat, layer the sandwiches as follows: one slice of rye (buttered side facing down), one slice of Swiss cheese, a cooked beef patty, a generous spoonful of caramelized onions, a drizzle of secret sauce, a slice of cheddar cheese, and top with a second slice of bread (buttered side facing up). Grill each sandwich until the bread is crisp and golden, about 1–2 minutes per side. Flip carefully and grill the opposite side until evenly browned and the cheese is melted.