Shredding your own Parmesan on the small or medium holes of a box grater is the key to this recipe. Finely shredded Parmesan (long thin strands) is essential here—it adheres well to the carrots and melts evenly into a thin, lacy crust that turns perfectly crisp. Grated Parmesan, pre-shredded Parmesan or larger shreds won’t achieve the same texture or melt in the same way.