Preheat oven to 350 degrees and grease your donut pans generously otherwise, the donuts will stick.
In a large bowl, mix the eggs, sugar, vanilla extract, milk, and melted butter, and set it aside.
In a separate bowl, sift the all-purpose flour, cocoa powder, baking powder, baking soda, and salt. Add to the wet ingredients.
Place the batter into a zippered plastic bag, cut the tip, and fill the greased donut pan 3/4s of the way.
Bake for about 8 minutes or until fully cooked through.
While the donuts bake, prepare the glaze. In a large bowl, combine the confectioners sugar, vanilla extract, and milk. Whisk until smooth.
Allow the donuts to cool for 12-15 minutes before frosting. I like to place one donut at a time in the icing and coat it on both sides but feel free to spoon the icing over the donuts instead.