Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder, salt, and cinnamon until combined.
In another bowl, whisk together the eggs, vegetable oil, and vanilla extract until well blended.
Add the wet ingredients to the dry ingredients and mix until just combined. Fold in the grated zucchini gently until evenly distributed.
Pour the batter into the prepared baking pan and smooth the top with a rubber spatula. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
While the cake is baking, prepare the cream cheese frosting. In a mixing bowl, beat the softened cream cheese and butter together until creamy.
Gradually add the powdered sugar and vanilla extract, mixing until smooth. If the frosting is too thick, add milk one tablespoon at a time until the desired consistency is reached.
Once the cake has cooled completely, spread the cream cheese frosting evenly over the top.
Cut into 12 pieces and serve.