For the Secret Sauce:

1. 1. In a small bowl, mix together ketchup, mayonnaise, and pickle relish until well combined. Adjust seasoning with salt or hot sauce to taste.

For the Patty Melts:

1. 2. In a skillet over medium heat, melt 1 tablespoon of butter. Add sliced onions and sauté until golden brown and caramelized (about 10-15 minutes). Set aside.
2. 3. Shape ground beef into four patties about 1 inch thick. Season both sides generously with salt and pepper.
3. 4. Increase skillet heat to medium-high and add another tablespoon of butter. Cook each patty for about four minutes per side until browned and cooked through.
4. 5. Spread secret sauce on one slice of rye bread. Place a beef patty on top, followed by sautéed onions and two slices of Swiss cheese. Top with another slice of rye bread spread with butter.
5. 6. In the same skillet, grill assembled patty melts over medium heat until both sides are golden brown and cheese is melted (about three minutes per side). Serve hot with extra secret sauce drizzled on top.