Preheat oven to 375℉. Spray a 15x10x1" baking pan heavily with non-stick cooking spray.
In a large bowl, cream sugar and yogurt together until smooth. Add eggs, beating after adding each one.
In a separate bowl, sift flour, cocoa powder, baking soda, baking powder, and salt.
Mix dry ingredients with the sugar/yogurt mixture, and then slowly pour in the milk.
Fold in the zucchini and the vanilla and pour batter into the prepared baking pan.
Bake for 25 minutes or until a toothpick stuck in the middle of the cake comes out clean.
Frosting
In a saucepan over medium low heat, combine the butter, cocoa, and milk.
Heat to boiling, stirring frequently.
Remove from heat and mix in the powdered sugar and vanilla until the frosting is smooth (you may have to whisk it).
Pour warm frosting over brownies as soon as you take them out of the oven. Let cool completely before serving
Notes
Shred your zucchini using a box grater. Be sure to pour out any excess liquid from your zucchini after you shred it to make sure to get the right consistency, but there is no need to pat it dry.