Preheat oven to 350°F (175°C). Grease and flour a 9x9-inch baking pan.
In a medium bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt.
In a large bowl, beat together the oil, granulated sugar, and brown sugar until well combined.
Add the eggs and vanilla extract to the sugar mixture, beat until smooth.
Gradually add the dry ingredients into the wet mixture and mix until just combined.
Fold in the grated zucchini until evenly distributed.
Pour the batter into the prepared pan and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.
To make the frosting, beat the cream cheese and butter together until smooth. Gradually add the powdered sugar and vanilla extract, and beat until smooth and creamy.
Spread the frosting evenly over the cooled cake. Slice and serve for a delightful treat.
Notes
Store any leftovers in an airtight container in the refrigerator for up to 3 days.