Line a baking sheet with parchment paper or foil and either spray or give it a rub of butter.
Cut the parsnips into wedges or halves depending on the thickness. Since they taper so much, use the ends whole then cut the fat top into fourths. Try to get them as evenly sized as possible.
In a large bowl, beat the egg whites til frothy with 2 tsp dried oregano.
Working with about half of the parsnips at a time, toss in the egg white and then gently roll in the Parmesan cheese.