Preheat Air Fryer to 360˚F.
Place the chicken breasts on a cutting board or a work surface.
Slightly pound each chicken breast to an even thickness; DO NOT pound them thin.
To butterfly the chicken breasts, hold a sharp knife along the long side of the chicken breast.
Using a sawing motion, slice about ¾ of the way through, being careful not to cut all the way through.
Fold out the chicken like a book, and press down to flatten. Set aside.
In a mixing bowl combine the basil pesto, feta cheese, and garlic.
Divide the filling between the four chicken breasts.
Close them up and secure with toothpicks.
Rub the chicken breasts with the olive oil and season with salt, pepper, paprika, garlic powder, onion powder, and cayenne pepper.
Transfer to the Air Fryer and cook for 18 to 23 minutes, or until cooked through. Cooking time depends on the size of the chicken breasts. Chicken is done when its internal temperature registers at 165˚F. Use a meat thermometer and start checking for doneness at around the 18-minute mark.
Remove from the air fryer and let stand for 5 minutes before cutting serving.