In a large mixing bowl, whisk egg, sugar, buttermilk, melted butter and vanilla together until smooth.
Sift in all dry ingredients and whisk until all incorporated.
Take out half the batter and pour it into a piping bag. Set aside.
Whisk in cocoa powder, melted chocolate and 1 Tbsp buttermilk into remaining batter. Whisk until smooth. Pour chocolate batter into another piping bag.
Cut the tips off both piping bags, leaving only about ½ inch opening.
Squeeze batter into the donut cups of the pan, using both bags at the same time (one in each hand), in the half-circle motion, making sure that half the donut is chocolate and the other half vanilla. Make sure there is an even amount of batter all around.
Bake for 10-11 minutes and let donuts cool on the wire rack, just until the donuts cooled enough to be handled.Spread paper towel under the cooling rack to catch icing drippings.
While donuts are cooling, prepare the icing.
Heat up all heavy cream and vanilla until hot but not boiling. Combine cocoa powder and 3/4 cup powder sugar in one bowl and place 1 cup of powder sugar in another bowl. Whisk in 4 Tbsp of hot heavy cream into chocolate mixture until all smooth. Whisk in 3 Tbsp of hot heavy cream into powder sugar in another bowl until all smooth.
You can either carefully dip top halves of donuts into icing or you can pour each icing over the donut halves with a spoon. I found it much easier to pour some icing over the donuts.