preheat oven to 400°F

Beat egg in large bowl. Stir in shallots, parsley, pepper and salt. Place shredded squash in the center of a clean kitchen towel; gather up ends and squeeze out liquid. Add the squash and cheese to the bowl; stir to combine

Heat oil in a large non-stick skillet over medium heat. Pack a 1/3 cup measuring cup with a the squash mix and unmold it into pan; gently pat down to form a 3 inch cake. Repeat, making 4 cakes. Cook until brown and crispy on the bottom, 3 to 4 minutes. Gently turn the cakes over and transfer the pan to the oven. Bake for 10 minutes. Serve immediately.