Prepare the Oven and Pan: Position a rack in the center of the oven, heat to 350 F, and grease and flour a 9-by-13-inch baking pan.

Combine Dry Ingredients: Sift the flour, cocoa, baking soda, baking powder, and salt into a bowl; set aside.

Start the Batter: In a mixing bowl with an electric mixer, beat the oil, butter, and sugar together for 2 minutes or until creamy and well blended. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla.

Finish the Batter: Add 1/3 of the flour mixture to the batter and beat just until combined. Beat in half of the buttermilk, then repeat with another 1/3 of the flour mixture and the remaining buttermilk. Add the remaining flour mixture and beat just until combined. Fold the zucchini into the batter.

Spread and Bake: Spread the batter in the prepared baking pan and bake for 32 to 38 minutes or until a toothpick inserted into the center of the cake comes out clean. Transfer the cake to a rack to cool completely. The cake should be cool when you make the frosting.

Make the Frosting and Finish the Cake: Combine the milk, butter, and sugar in a saucepan; bring to a boil over medium-high heat and boil for 1 full minute. Remove the pan from the heat and stir in the chocolate chips and vanilla until the chocolate has melted. Pour the hot frosting over the cooled cake. It will firm up to a soft, fudgy consistency in about 5 minutes.

Serve: Slice into squares and enjoy on its own or with a scoop of ice cream. Enjoy!