Preheat oven to 350 degrees F. Grease a 13x9-inch baking dish.
Start with the preparation of the cake. In a large bowl whisk the flour, sugar, cocoa, salt, baking soda, and baking powder.
In another large bowl, whisk together the eggs, milk, oil, and vanilla. Stir in the zucchini
Add the dry ingredients to the wet ingredients and stir. The batter will be very thick.
Spread batter into the baking dish. Bake at 350 degrees F for 35 minutes or until a toothpick is almost clean from the center. Allow cake to cool completely before frosting.
While cake is cooling, prepare the frosting. Use a hand mixer to beat the butter, cocoa, and vanilla in a large bowl. Slowly add the powdered sugar, then 2 Tablespoons of milk, and a pinch of salt. Add more milk a tablespoon at a time until desired consistency is reached. You want the frosting to spread easily over the cooled cake. Spread frosting over cake and serve.