Preheat your oven to 350°F (175°C) and grease the 9x13 inch baking pan.
In a large mixing bowl, combine the grated zucchini, vegetable oil, granulated sugar, brown sugar, eggs, and vanilla extract. Mix well until fully combined.
In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
Gradually add the dry mixture to the wet mixture, stirring gently with a rubber spatula until just combined. Be careful not to overmix.
Pour the batter into the prepared baking pan and smooth the top. Bake in the preheated oven for 30-40 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
While the cake is cooling, prepare the cream cheese frosting. In a mixing bowl, beat the softened cream cheese and butter together until smooth.
Gradually add the powdered sugar and mix until well combined. Add in the vanilla extract and milk, adjusting the milk as needed to reach your desired frosting consistency.
Once the cake is completely cooled, spread the cream cheese frosting over the top using a spatula.
Slice and serve, enjoying the delightful combination of moist cake and rich frosting.