Parboil whole potatoes in salted water for 10 minutes until just tender when pierced. Drain and let cool completely.
Peel cooled potatoes and grate using the large holes of a box grater into a large bowl.
Grate onions on the same grater and add to the potato mixture.
Place grated potato and onion in a clean kitchen towel and squeeze firmly to remove as much liquid as possible.
Return the mixture to the bowl and add egg whites, melted butter, dried herbs, and paprika. Mix until evenly combined.
Shape into a round patty about 8 inches wide and 1 inch thick, pressing firmly so it holds together.
Preheat the air fryer to 390°F for 3 minutes.
Spray the air fryer basket lightly with oil and place the rösti patty in the basket.
Lightly spray the top of the patty with oil (about 3 seconds).
Cook at 390°F for 25 minutes, checking at 20 minutes if your air fryer runs hot.
Remove when the crust is deep golden brown. Rest 3 minutes before slicing.