To make the special sauce, in a small bowl, combine mayonnaise, ketchup, pickle juice, yellow mustard, Worcestershire sauce, and salt and pepper to taste. Set aside.
To make the quesadillas, in a large skillet over medium-high heat, cook ground beef until browned and cooked through, about 6 to 8 minutes. Drain well.
Wipe out the skillet, coat with nonstick spray, and heat over medium heat. Working with 1 flour tortilla at a time, add to skillet. Top half the quesadilla with ½ cup cheddar cheese, and ¼ of the cooked beef. Top with dill pickle chips, if using.
Sprinkle the top half of the tortilla with another ½ cup cheddar cheese. Fold in half and cook until cheese is melted and tortilla is golden brown on one side, about 2 minutes.
Flip the quesadilla and continue cooking until all the cheese is melted and the second side is golden brown. Transfer to a plate and cover to keep warm.
Repeat with the remaining tortillas, cheese, beef, and pickles. Cut each quesadilla in half and stack 2 halves on each of the 4 plates.
To make the wedge salads, add one wedge of Iceberg lettuce to each plate and top with shallots and cherry tomatoes. Drizzle the quesadillas and salad with sauce. Serve more sauce on the side if desired.
