Mix together the salt, thyme, rosemary, pepper, sage, garlic powder, paprika and brown sugar in a small bowl.
Brush the turkey breast with olive oil and rub on both sides with the dry rub mixture, making sure to get under the skin wherever possible. Put the turkey skin-side down in the basket of a 3.5-quart air fryer and roast at 360 degrees F for 20 minutes.
Carefully open the air fryer and flip the turkey over so it is skin-side up. Close the air fryer and roast until an instant-read thermometer inserted into the thickest part of the meat registers 165 degrees F, about an additional 15 minutes. Let rest at least 10 minutes, then slice and serve.
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