Parmesan-Squash Cakes

Preheat oven to 400°F. Beat egg in a large bowl. Stir in shallots, parsley, salt and pepper. Place shredded squash in the center of a clean kitchen towel; gather up the ends and twist to squeeze out any liquid. Add the squash and cheese to the bowl; stir to combine. Heat oil in a large nonstick skillet over medium heat. Pack a 1/3-cup measuring cup with the squash mixture and unmold it into the pan; gently pat it down to form a 3-inch cake. Repeat, making 4 squash cakes. Cook until browned 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.