Preheat oven to 350 degrees F. Grease and flour a 9x13 inch baking dish.
In a large bowl, mix together the oil, applesauce, 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. Spread evenly into the prepared pan. My zucchini was really moist but if yours is on the drier side, press the mixture into the pan. The zucchini will release moisture as it bakes.
Bake for 25 to 30 minutes in the preheated oven, until brownies spring back when gently touched.
For the frosting: Melt together the 6 tablespoons of cocoa and margarine and set aside to cool. In a medium bowl, blend together the confectioners' sugar, milk and 1/2 teaspoon vanilla. Stir in the cocoa mixture. Spread over cooled brownies before cutting into squares.