Whisk sugar, oil, vanilla, and grated zucchini in a mixing bowl till blended. Stir in remaining brownie ingredients. Spread into a greased 9×13-inch pan.
Bake at 350f degrees for 30-35 minutes or till toothpick comes out clean. Frost with chocolate frosting either while warm or cooled.
To prepare frosting: Beat together butter and cocoa till smooth. Beat in remaining ingredients, adding milk until your desired consistency.