Preheat your oven to 350°F (175°C) and grease and flour a 9x13 inch baking pan.
In a large mixing bowl, combine the grated zucchini, sugar, vegetable oil, eggs, and vanilla extract. Mix well until all ingredients are combined.
In another bowl, sift together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to over-mix.
Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool completely in the pan on a wire rack.
While the cake is cooling, prepare the cream cheese frosting by beating together the softened cream cheese and butter until smooth and creamy.
Gradually add the powdered sugar and 1 teaspoon of vanilla extract to the cream cheese mixture, mixing until well combined and fluffy.
Once the cake is completely cool, spread the cream cheese frosting evenly over the top.
Cut into squares and serve.