Preheat air fryer to 360°. Using a mandoline or vegetable peeler, cut potatoes into very thin slices. Transfer to a large bowl; add enough ice water to cover. Soak for 15 minutes; drain. Add more ice water and soak another 15 minutes.

Drain potatoes; place on towels and pat dry. Spritz potatoes with cooking spray; sprinkle with salt. In batches, place potato slices in a single layer on tray in greased air-fryer basket. Cook until crisp and golden brown, 15-17 minutes, stirring and turning every 5-7 minutes. If desired, sprinkle with parsley.