Cover 1 side of each bread slice thoroughly and generously with butter; set aside.
Mix ground beef, pepper, salt, and onion powder together in a bowl until thoroughly combined, but do not overmix or meat will not have the proper consistency after it is cooked. Form 3 patties to fit the shape of the bread.
Heat a large nonstick skillet over medium-high heat. Add patties and cook for 2 to 3 minutes. Flip, making sure patties do not break, and cook for another 2 to 3 minutes. Reduce heat to low, and cook until no longer pink in the centers, about 5 minutes more. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C).
While the burgers are cooking, combine mayonnaise, ketchup, bacon bits, relish, and sugar for sauce in a small bowl. Stir until mayonnaise and ketchup are well binded.
Heat another large skillet over medium-low heat. Place 1 slice bread in the skillet, buttered-side down. Top with 2 slices Cheddar cheese, a cooked patty, and 2 slices provolone cheese. Spread a thin layer of sauce on the unbuttered side of a second slice of bread, and place sauce-side down on top of provolone. Repeat to make remaining patty melts, working in batches if necessary.
Cook until bread is lightly toasted and cheese is melted, 2 to 3 minutes per side.