Divide the beef in half. On a sheet of waxed paper, shape each half into a 4-inch patty (about 1/2 inch bigger than the bun in diameter). Season both sides with salt. Place, uncovered, in the freezer for 5 minutes.

Preheat a large nonstick skillet over medium-high heat until drops of water sizzle when splashed on the pan. Place the patties in the pan. Cook for 1 to 2 minutes per side, or until no longer pink. Meanwhile, place the bun top and bottoms, cut-sides down, in the pan. Cook for about 1 minute, or until toasted. Just before the patties are cooked, place the cheese on 1 patty (only one of the two patties per burger gets cheese, just like the original).

Place 1 bun bottom on a plate. Spread on 1 tablespoon sauce. Place the cheeseburger, cheese-side down, on the bun. Spread 1 teaspoon sauce on the second bun bottom and place, sauce-side down, on the cheeseburger. Top with the remaining 1 tablespoon sauce, the onion, lettuce, pickles, the remaining burger, and the bun top.

Combine the mayonnaise, relish, ketchup, sugar, and mustard in a small bowl. Stir to blend well. Cover and refrigerate for up to 1 month. Stir in the onion just before serving. Makes about 2/3 cup, enough for 4 servings.