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1
Place 1/3 cup of the warm milk in the bowl of an electric mixer. Stir in the yeast and let sit for five minutes. If yeast does not bubble up, discard and start again with fresh yeast. Meanwhile, stir the butter into the remaining warm milk to melt it. Whisk together the sugar, cocoa powder, espresso powder, flour, and salt.
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2
To the softened yeast, add the dry ingredients, the remaining milk with melted butter, the vanilla extract, and lightly beaten egg and mix together with the paddle attachment of your mixer to combine. Switch to the dough hook and continue mixing until dough is smooth and pulling away from the sides of the bowl, adding more flour if dough is sticky or more milk if too dry.
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3
Turn dough out onto a lightly-floured surface and knead a few times (dough should be barely sticky), shape into a ball and place in an oiled boil, turning to coat the dough with oil. Cover the bowl and let the dough rise in a warm place until doubled, about 1-2 hours.
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4
Punch dough down and roll it out onto a lightly-floured surface to 1/2-inch thickness. Cut out 4-inch circles and transfer them to parchment-lined cookie sheets. Then cut out 2 1/4-inch circles from the centers. Loosely cover the donuts with plastic wrap.
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5
At this point, you may either let the donuts rise for 45 minutes and proceed to bake them, or refrigerate them overnight. After refrigeration, let donuts rise 1 hour in a warm place. Bake at 375 F for 8-10 minutes, then let cool for about 10 minutes.
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6
While donuts are baking, place the butter and whole milk in a small saucepan and place over medium-high heat, whisking constantly to melt butter and prevent the milk from burning. As soon as the milk reaches a boil, remove from heat and add chocolate chips, whisking until chocolate melts and the ganache is smooth and glossy. Let cool slightly.
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7
To glaze the donuts, invert each donut and dip into the chocolate ganache, allowing the excess chocolate to drip off before setting the donuts upright.
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8
Makes ~10 donuts and 10 donut holes.
