Preheat your oven to 350°F (175°C) and grease the 9x13 inch baking pan.
In a mixing bowl, combine the flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Whisk to blend the dry ingredients well.
In another bowl, beat together the granulated sugar, vegetable oil, eggs, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated zucchini until evenly distributed throughout the batter.
Pour the batter into the greased baking pan and spread it evenly. Bake in the preheated oven for 35-40 minutes or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool completely in the pan on a cooling rack.
While the cake is cooling, prepare the cream cheese frosting. In a mixing bowl, combine the softened cream cheese and softened butter. Beat together until creamy and smooth.
Gradually add the powdered sugar and mix until fully incorporated. Add the milk and vanilla extract, beating until the frosting reaches a spreadable consistency.
Once the cake is completely cool, frost the top with the cream cheese frosting using a spatula.
Slice into pieces and serve.