Grate zucchini with a cheese grater or food processor. Spread out onto a double layer of paper towels. Sprinkle with salt. Let sit at least 15 minutes to draw out moisture. Pat dry and then wrap zucchini in dry towels and squeeze to remove as much moisture as possible. May be done 1-3 days in advance and stored in paper towels in a ziplock bag in refrigerator.
On a greased sheet pan or parchment lined, place a small pile of cheese, about 1 inch in diameter. Top with grated zucchini and then more cheese, using a ratio of half zucchini : half cheese. Sprinkle with a touch of red pepper if desired.
Bake at 400 degrees until cheese has melted and started crisp. Let cool on pan 1-2 minutes to set up. Remove to paper towel to drain and then serve immediately
I made these 2 ways, all Parmesan and then half Parmesan, half cheddar. Both were good but cheddar has more fat so releases more oil. I preferred the drier Parmesan.