Preheat the oven to 350 degrees. Mist a 9 x 13-inch baking dish and set aside.
In a large bowl, beat the oil and sugars using an electric hand mixer or stand mixer until smooth. Add the eggs, whisking after each addition. Add the vanilla and beat until well-combined.
In another mixing bowl, whisk together the flour, baking powder, soda, cinnamon, and salt. Add to the egg mixture and beat on low speed until no white streaks remain. Fold in the shredded zucchini and pour into the prepared baking dish. Bake for 35-40 minutes or until an inserted toothpick is removed cleanly.
Meanwhile, beat together the cream cheese, butter, vanilla, and milk. Add the powdered sugar, beating on medium-low speed until smooth and fully incorporated.
Once cake has cooled completely, spread the frosting evenly over the surface of the cake. Refrigerate until serving.