Brine the chicken parts first. Add ¼ cup salt to a bowl (or zipper-closure bag) of slightly warm water. Add the chicken thighs or breasts and let them sit in this brine for 15 minutes.
While the chicken is brining, combine the seasonings for the rub.
Drain the salt water mixture, rinse the chicken with cool water and thoroughly pat dry.
Toss the chicken parts with 1 tablespoon olive oil, then rub the spice mixture into both sides.
For bone-in, skin-on chicken thighs, air fry at 375°F. for 8 minutes, then pause the air fryer and remove the basket. Use tongs to flip the pieces over. For boneless, skinless breasts, air fry at 375°F. for 6 minutes.
Place a tablespoon or so of grated parmesan cheese on top of each of hte pieces of chicken. Return the basket to the fryer and fry at 350°F. for 4 minutes (both thighs and breasts.) With an instant-read meat thermometer, check that the internal temperature of the chicken has reached 165°F.
Remove with tongs and serve.
For boneless, skinless chicken thighs, follow the directions for boneless, skinless chicken breasts.