Preheat the oven to 350°F. Lightly greasy two standard 6-cavity doughnut pans
. In a large bowl, whisk together the cocoa powder, flour, sugar, baking powder, baking soda, and salt. In a medium bowl whisk together the eggs, milk, vanilla, and vinegar. Add to the dry ingredients with the melted butter and stir until combined. Scoop the batter into a zip-top plastic bag or piping bag, cut a hole in one corner, and pipe the batter into the doughnut molds, filling about 3/4 full. Bake for 12 to 15 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pans for 2 minutes before flipping the pans upside down over a rack to remove the doughnuts.