Preheat your oven to 350 degrees. Prepare a jelly roll pan by spraying it with cooking spray.
Whisk together in a large bowl the flour, baking powder, baking soda, and spices.
Whisk the eggs and sugars together in a large bowl until the sugars are just about dissolved. Now add the oil about a half a cup at a time and whisk in until it’s combined.
Slowly add the flour mixture. Stir in the zucchini. Pour into the pan and bake for 20 to 25 minutes or until a toothpick inserted into the center of the pan comes out clean. Allow to cool completely.
Beat together the butter, milk, cocoa powder, powdered sugar, and vanilla until smooth. Gently spread over the sheet cake.