In a large bowl, cover the shredded potato with cold water and stir to rinse; drain and transfer to a towel-covered work surface. Cover with another towel and roll up to remove excess moisture; rinse and dry the bowl. Squeeze the carrots and zucchini in another towel to remove excess moisture. In the bowl, combine the potato, carrots, zucchini, onion, egg and egg white, flour, cornstarch, baking soda, 3/4 teaspoon salt and 1/4 teaspoon pepper.
Heat a large skillet for 1 minute over medium-high heat. Add 1 tablespoon olive oil and swirl to coat. Working in batches, and using the remaining 1 tablespoon olive oil when necessary, spoon 1/4 cupfuls of the veggie mixture into the pan and flatten into 3-inch pancakes. Fry until golden underneath, about 3 minutes. Flip, sprinkle a bit of cheese on top of each and cook for about 2 minutes more; transfer to a plate.