Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large mixing bowl, combine the grated zucchini, oil, sugar, eggs, and vanilla extract. Mix until well blended.
In another mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour the batter into the prepared baking pan, spreading it evenly.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan on a cooling rack.
While the cake is cooling, prepare the cream cheese frosting. In a mixing bowl, beat the softened cream cheese and butter until smooth and creamy.
Gradually add the powdered sugar and vanilla extract. Mix until combined. If the frosting is too thick, add milk one tablespoon at a time until you reach the desired consistency.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top of the cake.
Slice into squares and serve. Enjoy!