Prepare the Sauce: In a small bowl, combine mayonnaise, ketchup, bacon bits, sweet relish, and sugar. Mix well and set aside. This creamy sauce will add a tangy and slightly smoky flavor to your patty melts.

Make the Beef Patties: Divide the ground beef into 3 equal portions (about 5.3 ounces each) and shape them into thin, oblong patties slightly larger than your rye bread slices (they will shrink while cooking). Season the patties evenly with salt, black pepper, and onion powder.

Cook the Patties: Heat a skillet or griddle over medium-high heat. Place the beef patties in the skillet and cook for about 3-4 minutes per side, or until cooked through with a nice sear. Transfer the patties to a plate and let them rest.

Assemble the Patty Melts: Butter one side of each slice of rye bread. On the unbuttered side of 3 slices, spread a thin layer of the prepared sauce. Place a slice of cheddar cheese, a cooked beef patty, a slice of provolone cheese, and another slice of rye bread (buttered side facing up) on top. Repeat for all sandwiches.

Grill the Patty Melts : Heat a clean skillet or griddle over medium heat. Place the assembled sandwiches in the skillet. Cook for 3-4 minutes per side, pressing gently with a spatula, until the bread is golden brown and crispy and the cheese is melted.

Serve: Slice the patty melts in half and serve warm with extra sauce on the side, if desired.