Preheat oven to 350 degrees F. Spray a 9x9 inch baking pan with nonstick spray.
In a medium bowl, combine sugar, flour, cocoa powder, baking soda and salt. In a large bowl mix together applesauce, egg, vanilla extract, then fold in zucchini. Mix in the flour mixture slowly until all blended. Spread evenly into the prepared pan.
Bake for 30-45 minutes in the preheated oven, until toothpick comes out clean when pricked into the center. Allow brownies to completely cool before frosting.
To make the frosting: In a medium bowl, blend together soften butter and cocoa powder. Slowly blend in confectioners sugar and milk, alternating. Then blend in vanilla.
Cut brownies into squares and smother them in frosting. Enjoy!