Preheat oven to 350 degrees F. Grease a 9x13'' pan.
In a large mixing bowl beat together the oil and sugar.
Add the egg and mix well. Add the vanilla and shredded zucchini and mix well.
In a separate bowl mix together the flour, cocoa powder, baking soda, baking powder and salt.
Add dry ingredients to the large mixing bowl and beat until combined.
Spread mixture into prepared pan (batter will be thick) and smooth into an even layer.
Bake for 30-35 minutes or until they center of the brownies springs back when gently touched. Cool on a wire cooling rack.
Frost brownies with cream cheese frosting once they are completely cool.