Preheat oven to 350°F. Grease a 9x13-inch baking pan and set aside.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt and cinnamon.
In a large bowl, whisk together the eggs, oil, sugar, and vanilla extract.
Add the dry ingredients into the wet and whisk to combine. Add the zucchini and fold to combine.
Transfer mixture to the baking pan and bake for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool completely before frosting.
To make the frosting, add the cream cheese and butter to a large bowl and use a hand mixer to beat until smooth. Add in the powdered sugar and mix on low to combine. Add in the vanilla and milk, increase speed to medium and beat until fluffy and well incorporated, about a minute or so.
Transfer to finished cake and smooth frosting over the entire surface. Slice up and enjoy!