Preheat oven to 350°.
Combine flour, sugar, cocoa, baking soda, baking powder, and salt in a bowl; then, add milk, applesauce, vinegar, and vanilla to that same bowl and stir with an electric mixer until combined.
Last, stir in the zucchini by hand.
Grease three 8" cake pans with coconut oil and divide the batter evenly amongst the pans. Bake the cakes for 30-35 minutes, or until a toothpick comes out clean. Allow the cakes to sit in the pans for 10 minutes, and then run a knife along the edges of the cake and carefully invert them onto a cooling rack. Wait until cakes have completely cooled before icing them.
For the buttercream: cream butter and milk together, then add cocoa and powdered sugar. You want the icing to be thick but still spreadable. If it seems too thick, add 1 tablespoon milk. If it seems too thin, add 1/4 cup powdered sugar.
To assemble: use a serrated knife to remove domes off of the cakes, then scoop a large dollop of icing onto the first cake and spread it; then place the second cake on top of that cake and repeat that same step. Top the final layer with chocolate chips or chopped chocolate, if you want.