In a large bowl, sift together the flour, cocoa, sugar, baking powder, salt, and espresso powder (if using) and make a well in the centre of the dry ingredients. In a separate bowl, whisk together the buttermilk, egg, melted butter, and vanilla. Pour this wet mixture into the well and mix just until a soft dough forms. Cover your bowl with plastic wrap and refrigerate the dough for one hour.
Remove the dough from the fridge and heat about five centimeters of vegetable oil in a large, deep pot over medium heat until a thermometer registers at 350F. On a generously floured work surface, roll out your chilled dough to a six millimeter thickness and, using a two centimeter round cutter, cut out your doughnut holes.
Feel free to bring the remaining dough together to reroll and cut out more doughnut holes but only do this once as rerolling the dough a third time might make them a bit tough.
Before frying, prepare a draining station for your doughnut holes by lining a cookie sheet with paper towel and a cooling rack.
Now, it’s time to fry! Gently lower seven or eight doughnut holes into the hot oil and cook for around three to four minutes, flipping occasionally. Remove the cooked doughnut holes to the rack-lined cookie sheet and continue to fry until all of your doughnut holes are done.
When cooled, dunk each doughnut and doughnut hole in vanilla glaze and serve.
For the vanilla glaze:
In a small bowl, mix the icing sugar with the vanilla and warm water until smooth. If the glaze looks too thin, add a bit more icing sugar. If it looks too thick, add a touch more water.