Preheat the oven to 425 degrees . Coat a large rimmed baking sheet with natural cooking spray. In a medium bowl, toss parsnips and flour to coat. In another medium bowl, beat eggs with a fork. In a third medium bowl, stir panko and cheese. Working with a few parsnip sticks at a time, shake off excess flour and coat with egg mixture. Shake off excess egg and roll in panko mixture. Arrange in a single layer on the baking sheet. Bake 15 minutes, then turn the fries and bake until golden, 10 to 12 minutes; season.