A good substitute for shredded Parmesan cheese is grated pecorino romano. This aged, hard cheese has a sharp and tangy flavor that works well in both hot and cold dishes. Asiago is another good option with a nutty flavor. For a milder flavor, try using grated cheddar or jack cheese. These cheeses don’t have the same sharpness as Parmesan but will add a creaminess and nuttiness to your dish.