Preheat the oven to 350°F and grease a 9×13 inch baking pan with nonstick cooking spray.
Wash and trim the zucchini and grate with the large holes of a box grater until you have 2 cups. Set aside.
In a large mixing bowl, vigorously whisk together the granulated sugar, vegetable oil, eggs and 1 tablespoon vanilla extract until smooth and combined.
Add the all purpose flour, cinnamon, baking soda, baking powder, salt, and nutmeg. Using a rubber spatula, gently fold the dry ingredients into the wet just until combined. Do not overmix.
Fold in the grated zucchini (and chopped nuts, if using) until evenly distributed throughout the batter.
Pour batter into the prepared baking pan and smooth into an even layer.
Bake for 35-40 minutes or until a toothpick inserted in the center of the cake comes out clean.
Let the cake cool in the pan on a wire cooling rack until completely cooled to room temperature.
To make the frosting, beat the softened cream cheese and softened butter together on medium high speed with an electric mixer until light, fluffy, and smooth, about 2-3 minutes.
With mixer speed reduced to low, slowly add the powdered sugar and mix until incorporated. Add the vanilla extract and a tiny pinch of salt. Beat on medium high speed for 1 more minute until fluffy.
Spread the cream cheese frosting evenly over the completely cooled cake. Cut into squares and serve.