Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan or line it with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder, cinnamon, and salt until well combined.
In a separate bowl, beat the eggs, vegetable oil, and vanilla extract until smooth. Add the grated zucchini and mix well.
Gradually add the wet ingredients to the dry ingredients and mix until just combined. Do not overmix.
Pour the batter into the prepared 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. Let the cake cool in the pan for 10 minutes before transferring it to a cooling rack to cool completely.
While the cake cools, prepare the cream cheese frosting. In a medium bowl, beat the softened cream cheese and butter together until smooth.
Gradually add the powdered sugar, mixing well after each addition. Add the vanilla extract and enough milk to reach the desired spreading consistency.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.
Slice the cake, serve, and enjoy!