Prepare the Sloppy Joe Mixture:

In a large skillet over medium-high heat, cook the ground beef and chopped onion until the beef is browned and the onion is tender. Drain excess fat.
Stir in ketchup, mustard, Worcestershire sauce, brown sugar, salt, and pepper. Simmer for 10 minutes until the mixture is thick and flavorful.
Make the Special Sauce:

In a small bowl, combine mayonnaise, French dressing, sweet pickle relish, minced onion, white vinegar, sugar, and salt. Mix until smooth and set aside.
Assemble the Sloppy Joes:

Preheat your oven to broil. Split the hamburger buns and place them on a baking sheet, cut side up. Toast under the broiler for 1-2 minutes until golden brown.
Place a slice of cheddar cheese on the bottom half of each toasted bun.
Spoon a generous amount of the Sloppy Joe mixture over the cheese.
Add another slice of cheddar cheese on top of the Sloppy Joe mixture.
Top with shredded lettuce and dill pickle slices.
Drizzle with the special sauce.
Place the top half of the bun on top.
Serve:

Serve your Big Mac Sloppy Joes with extra special sauce on the side for dipping.