Grate your zucchini and place in a kitchen towel or cheesecloth. Using your hands, squeeze out all the moisture from the zucchini. Place the zucchini in a mixing bowl.
Grate your carrot next and add to the bowl. Add your egg, flour, parmesan cheese, garlic powder, salt and pepper. Then using a spoon, mix until well combined.
Heat about a tablespoon of olive oil on a non-stick pan or skillet. Then scoop about 1/4 cup of the fritter batter, and flatten gently using the back of the spoon to form round shapes. Cook for about 2-3 minutes until browned. Then flip and cook for another 2 minutes or so.
Transfer to a plate and cook the rest of the fritter mixture. To serve, top with tomato sauce or greek yogurt.
For storage, place in an airtight container in the fridge or freeze for longer storage.