Bash together the garlic and anchovies using a pestle and mortar to create a thick paste. Transfer to a bowl and stir in the mayonnaise, parmesan, mustard and a splash of the leftover giardiniera pickling liquid. Season with salt, pepper and a bit more pickling liquid, if needed.
Spread the dressing over the tortillas, leaving a border, then dot over the sliced chicken leftovers, lettuce and the leftover drained giardiniera. Wrap up tightly, folding the ends in so everything stays in place.
