Preheat oven to 350 °F and prep a 9x13 inch baking dish with cooking spray or butter.
In a large mixing bowl, whisk together the flour, cocoa powder, baking soda, salt and sugar. Create a well or nest in the center of the dry ingredients and pour in the melted butter, buttermilk, vanilla extract, and eggs. Using a spatula or wooden spoon stir for 10 seconds, then fold in the grated zucchini. Continue mixing until no flour pockets remain.
Place into a buttered (or sprayed) 9x13-inch baking pan. Place in the oven and bake at 350°F for 25-28 minutes. Remove from the oven and allow to cool.
Meanwhile, to make the frosting, in a medium saucepan set over low heat, melt the butter, then add the milk and sifted cocoa powder. Stir to combine, then remove from the heat and add the vanilla extract and the sifted powdered sugar. Spread over the slightly warm cake. Allow to cool and set for 30 minutes before slicing and serving.