To make the special sauce, in a small bowl, combine mayonnaise, ketchup, pickle juice, mustard, Worcestershire sauce, and salt and pepper to taste (I like 1/2 teaspoon salt and 1/4 teaspoon pepper). Set aside.
To make the quesadillas, in a large skillet over medium-high heat, cook beef until browned and cooked through, about 6 to 8 minutes. Drain well.
Wipe out skillet, coat with nonstick spray, and heat over medium heat. Working with 1 tortilla at a time, add to skillet. Top half the quesadilla with 1/2 cup cheese, 1/4 of the cooked beef. Top with pickle slices, if using,
Sprinkle top half with 1/2 cup cheese. Fold in half and cook until cheese is melted and the tortilla is golden brown on one side, about 2 minutes.
Flip 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 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 to each plate and top with shallots and tomatoes. Drizzle the quesadillas and salad with sauce. Serve more sauce on the side if desired.