To make the special sauce, combine the mayonnaise, ketchup, pickle juice, mustard, Worcestershire sauce, salt, and pepper in a small bowl. Stir until smooth and set aside.
To make the quesadillas, cook the ground beef in a large skillet over medium-high heat for about 6 to 8 minutes, until browned and cooked through. Drain the beef well.
Wipe out the skillet, lightly coat it with nonstick spray, and heat over medium heat. Place one tortilla in the skillet.
On one half of the tortilla, sprinkle ½ cup of shredded cheese. Add ¼ of the cooked beef on top of the cheese. Add pickle slices if using. Sprinkle another ½ cup of cheese over the beef.
Fold the tortilla in half. Cook for about 2 minutes, until the bottom is golden brown and the cheese starts to melt. Flip carefully and cook until the second side is golden brown and the cheese is fully melted.
Transfer to a plate and cover to keep warm. Repeat with the remaining tortillas, beef, cheese, and pickles. Cut each quesadilla in half and place two halves on each plate.
For the wedge salads, place one wedge of Iceberg lettuce on each plate. Top with chopped shallots and cherry tomatoes. Drizzle both the quesadillas and the salad with the special sauce. Serve extra sauce on the side if desired.