Preheat oven to 350 degrees. Grease and flour a 9 x 13-inch baking dish.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and ground nutmeg. In a separate large bowl, stir together the grated zucchini, eggs, vegetable oil, granulated sugar, brown sugar, and vanilla extract. Add the flour mixture to the zucchini mixture in several intervals mixing just until combined. Fold in the chopped walnuts.
Pour batter into the prepared baking dish. Bake for 35-40 minutes or until a toothpick inserted in the center comes out clean or with a few moist crumbs. Do not over-bake; start checking at 35 minutes and every 3 minutes thereafter. Cool completely.
Using a stand mixer with a paddle attachment, beat together the butter, cream cheese, cinnamon, and vanilla until light, fluffy and smooth. Turn the mixer to low and gradually add the powdered sugar, beating until well combined. Scrape down the bowl and beaters as needed. Spread on the fully-cooled cake.
This cake should be refrigerated because of the cream cheese frosting.
