Preheat oven to 350°. Grease and flour a 9x13 inch baking pan.
In a large bowl, mix together the oil, sugar and 2 teaspoons vanilla until well blended. Combine the flour, 1/2 cup cocoa, baking soda and salt; stir into the sugar mixture. Fold in the zucchini. If really dry allow to sit for a few minutes so the zucchini releases some moisture. Spread evenly into the prepared pan.
Bake for 25 to 30 minutes in the preheated oven, until brownies spring back when gently touched.
Make frosting while brownies cool. Melt together the 6 tablespoons of cocoa and butter; set aside to cool.
Blend together the powdered sugar, milk and 1 teaspoon vanilla. Stir in the cocoa mixture. Spread over cooled brownies before cutting into squares.