Marinate chicken in pickle brine in the refrigerator for 30 minutes; this is included in prep time. Drain and pat dry, then unfold the thighs so they lie evenly.
Preheat a 6-quart air fryer to 390°F for 3 minutes. Beat egg with water and mix flour, cornmeal, salt, paprika and pepper in a separate bowl.
Dip chicken in egg, press into the cornmeal mixture and dab with oil until no dry patches remain. Arrange both thighs in the basket without touching.
Air fry for 8 minutes, turn and cook for 8 to 10 minutes more until crisp and at least 165°F. Rest on a rack for 3 minutes.
Spread mayonnaise on the buns and add dry lettuce, chicken and pickle slices. Close and serve one sandwich per person.