Preheat the oven to 350 degrees and spray a 9x13 baking pan with non stick cooking spray.
In a medium bowl add the flour, baking soda, baking powder, salt, cinnamon and nutmeg and whisk until combined.
In a large bowl add the eggs, vegetable oil,sugars and vanilla extract and whisk until combined.
Add the dry ingredients into the wet ingredients and using a spoon mix until combined. The batter will be on the dryer side.
Fold in the shredded zucchini and mix until incorporated. The water from the zucchini will add the moisture the batter needs.
Spread the batter into the prepared baking pan and bake for 28-30 minutes or until a toothpick comes out clean.
In a medium bowl add the room temperature butter and cream cheese and using a hand mixer beat until smooth. Add in the powdered sugar and beat until combined making sure to scrape down the sides with a spatula.
Let the cake cool completely then spread the cream cheese frosting over the top and sprinkle the walnuts on.