Preheat your oven to 350 degrees F. Spray your doughnut pan with cooking spray and set aside. In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda and salt.
In a medium saucepan, set over medium heat, add the butter. When melted, add the chocolate chips and espresso powder. Allow to stand and melt for a minute or two and then mix with a spatula until smooth. Turn the heat off and then stir in the sugar and egg yolk. Lastly, whisk in the buttermilk and vanilla extract.
In one batch, add the wet ingredients to the dry and mix just until you no longer see any speckles of flour. Fill the doughnut pan half way. Transfer the doughnuts to the oven to bake for 12 to 15 minutes, until firm to the touch. Allow to cool in the doughnut pan for a minute or two and then run a butter knife along the outside, lifting them out of the pan with your fingers. Transfer them to a cooling rack while you make the frosting.
Meanwhile, in a medium bowl, whisk together the powdered sugar, cocoa powder, vanilla extract and 2 tablespoons of milk. Add more milk or water, one tablespoon at a time, until it reaches a thick yet pourable consistency. If you like, you can add the corn syrup. This is not mandatory and was only used to give it that beautiful sheen—feel free to skip it! Dip the doughnuts, one at a time, into the frosting and place back on the cooling rack. Top with a liberal amount of sprinkles. Doughnuts will stay delicious for up to 3 days when kept in an airtight container.