Preheat the oven to 350 degrees F. Grease a 6-cup donut pan with non-stick cooking spray. In a large bowl, combine the cocoa powder, flour, brown sugar, baking powder, baking soda and salt. In a medium bowl, whisk together the eggs, milk, vanilla extract and vinegar.

Fold the wet ingredients into the dry ingredients, along with the melted butter, until just combined. Transfer the batter to a piping bag or a Ziploc bag with a corner cut off, and pipe the batter into the pan. Bake for 12-15 minutes until a toothpick inserted into a donut comes out clean. Wait 1 minute before carefully removing the donuts from the pan and letting them cool on a wire rack. Bake the remaining batter in the donut pan.

Once the donuts have cooled completely, make the icing. Combine the chocolate chips and milk in a microwave-safe small bowl, and melt the mixture in 30-second blasts in the microwave, slowly stirring until smooth. Dip the tops of the donuts into the chocolate icing letting the excess drip back into the bowl. Decorate with sprinkles. Let the icing set for 1 hour before serving.