In a measuring cup, mix the milk and lemon juice. All it to set at room temperature.
In the bowl of a standing mixer fitted with a paddle attachment, add 1 cup flour, cocoa powder, sugar, baking powder, and salt.
Add the eggs and egg yolks and mix well.
Dissolve the espresso powder in the milk mixture.
Add the milk mixture, vanilla, and vegetable oil and mix until combined.
Add the remaining 2 cups of flour, and mix until just combined. The mixture will be wet.
Scrape the mixture on top of a piece of parchment paper.
Lay another piece of parchment over the dough. Roll out into about 1/2 in thick sheet.
Transfer the dough to a baking sheet. Place the dough in the fridge to rest for about 30 min (or for however long it takes for the dough to not stick to the parchment paper).
While the dough chills, heat at least 2 inches of vegetable oil a heavy-bottomed pot. Heat the oil to 350 degrees.
Using a 3 1/2 inch round cutter, cut out circles of dough. Using 1 1/2 inch round cutters, cut out the center of each doughnut.
Fry the doughnuts in batches, about 1 to 2 minute son each side.
Once the doughnuts are all on a cooling rack, make the glaze.
In a small bowl mix the powdered sugar and the milk.
While the doughnuts are still warm (but not hot) dip them into the glaze.
Eat immediately or store in an airtight container for 1 to 2 days.