In a small bowl, combine mayonnaise, ketchup, pickle juice, mustard, Worcestershire sauce, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Set aside.
In a large skillet over medium-high heat, cook beef until browned and cooked through, about 6 to 8 minutes. Drain well on paper towels if desired.
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 and 1/4 of the cooked beef.
Top with pickle slices, if using, and another 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, beef, and cheese.
Top each romaine half with some tomato, shallot, and a drizzle of mayonnaise dressing. Serve with quesadillas.
Cut each tortilla in quarters and divide among 4 plates. 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.