Preheat oven to 350 degrees. Grease and flour a 9x13 cake pan.
In a large bowl combine oil(applesauce), sugar, vanilla, and egg. Mix well. Add zucchini, set aside.
In a separate bowl, combine flour, cocoa, baking soda, and salt. Blend together.
Take the sugar-zucchini bowl and gradually add the dry ingredients, stirring well with each addition until all the dry ingredients are incorporated. (Make sure you stir well to break down the zucchini for the moisture needed for a brownie batter texture.) when the batter has a thick brownie consistency (not dry or runny), pour into prepared cake pan and carefully smooth to the edges.
Bake in preheated oven for 25-30 minutes (the top will spring back). Don't over-bake or the brownies won't be dense and crumbly! Remove from oven and cool completely before frosting.
Frosting: In a large microwave safe bowl melt butter. Add cocoa and using a hand mixer blend together. Alternately incorporate powdered sugar and milk, mixing well between each addition. Do this until desired taste and consistency is reached (a little more stiff so you can add vanilla extract). Add vanilla and mix. Frost cooled brownies.
(I like thick, dark, fudgy frosting, so I use minimal powdered sugar and milk to get that rich intensity. More sugar mellows the cocoa and more milk creates a less stiff frosting.)