Whisk together the black pepper, salt, and onion powder in a small bowl, then mix into the ground beef until evenly seasoned. Divide and shape the meat into three patties sized to match the rye slices. Preheat a nonstick skillet over medium-high heat, add the patties, and cook for 2–3 minutes per side until browned. Reduce heat to low and continue cooking for 5 minutes more, or until the center reaches 160°F (71°C).
While the patties cook, stir the mayonnaise, ketchup, bacon bits, relish, and sugar in another bowl until smooth. Spread softened butter on one side of each bread slice. In a clean skillet over medium-low heat, place a butter-side-down slice, top with two cheddar slices, one patty, and two Provolone slices. Spread sauce on the unbuttered side of a second slice and place it sauce-side down to complete the sandwich. Grill for 2–3 minutes per side, pressing gently, until the bread is golden and the cheese is melted. Repeat to assemble the remaining two sandwiches.