Preheat air fryer to 360°. Using a mandoline or vegetable peeler, cut potatoes into very thin slices. Place in a large bowl; add ice water. Soak for 15 minutes; drain. Add ice water again and soak for 15 minutes.
Drain potatoes; place on towels and pat dry. Spritz potatoes and air fryer basket with cooking spray. Sprinkle potatoes with with salt. Working in batches, place potato slices in a single layer in air fryer basket and cook until crisp and golden brown, 15-17 minutes, stirring and turning every 5-7 minutes. If desired, sprinkle with parsley.