Preheat the oven to 350 F. Lightly grease the inside of a 10-inch bundt pan or tube pan with cooking spray.
In a medium bowl whisk together the flour, cocoa powder, baking powder, baking soda, and salt. Set the dry ingredients aside.
In a large bowl combine the brown sugar, vegetable oil, melted butter, buttermilk, eggs, and 2 teaspoons vanilla extract. Whisk together until smooth.
Add the dry ingredients into the large bowl with the wet ingredients and mix gently until the batter comes together.
Add the zucchini and chocolate chips into the batter and fold them in until just combined. Do not overmix.
Pour the batter into the prepared pan. Bake for 40-45 minutes, until a toothpick inserted in the cake comes out clean.
Cool the cake in the pan for 15 minutes, then turn the cake out onto a wire rack to cool completely.
While the cake cools, in a medium bowl whisk together the powdered sugar, remaining 1 teaspoon vanilla extract, and 3 tablespoons milk until smooth. If the glaze is too thick, add the additional tablespoon of milk.
Drizzle the glaze over the cooled cake. Cut the cake and serve.