In a small bowl, combine cocoa and boiling water.
Whisk until smooth. Set aside.
In a large bowl, whisk together flour, powdered milk, baking powder, and baking soda. Set aside.
With an electric mixer, beat butter, sugar, and salt just until combined.
Add egg, egg yolks, and vanilla.
Mix well.
Add flour mixture alternately with buttermilk, beginning and ending with flour mixture.
Mix until smooth.
Turn out onto a lightly floured surface.
Roll dough to 1/3" thick.
Cover dough and let it rest for 15 minutes.
Line a sheet pan with parchment paper.
Cut out doughnuts.
Place them on prepared sheet pan.
Re-roll scraps.
Allow to rest before cutting.
Cover.
Allow to rest for 15 minutes.
While dough is resting, pour at least 2 inches of vegetable oil into an 8 quart soup pot.
Heat oil to 375 degrees F.
Carefully place doughnuts, one at a time, into hot oil, making sure not to overcrowd the pan.
When the doughnuts rise to the surface of the oil, cook 1 minute.
Flip doughnuts over.
Cook 1 more minute.
Use a slotted spoon to remove doughnuts from oil.
Drain thoroughly.