1) Preheat the oven to 350°F. Lightly grease the wells of two standard doughnut pans. If you don't have two pans, simply bake the batter in two batches.
2) In a large mixing bowl, whisk together the cocoa, flour, sugar, baking powder, espresso powder, baking soda, salt, and chocolate chips. Set aside.
3) In a large measuring cup or medium-sized mixing bowl, whisk together the eggs, milk, vanilla, and vinegar. You may notice some curdling of the milk; that?s OK.
4) Add the wet ingredients, along with the melted butter or vegetable oil, to the dry ingredients, stirring to blend; there's no need to beat the batter, just make sure everything is well-combined.
5) Spoon the batter into the prepared pan(s), filling them between 3/4 and full.
6) Bake the doughnuts for 12 to 15 minutes, or until a toothpick inserted into the center of one comes out clean.
7) Remove the doughnuts from the oven, and after 30 seconds or so, loosen their edges, turn the pan upside down over a rack, and gently let the doughnuts fall onto the rack.
8) For sugar-coated doughnuts, immediately shake the doughnuts in 1 tablespoon granulated sugar; add 1/2 teaspoon cocoa powder to the sugar for an additional touch of chocolate.
9) If you want to ice the doughnuts rather than shake them in sugar, allow them to cool completely before icing.
10) To make the icing: Combine the chocolate chips and milk or half & half in a microwave-safe bowl or measuring cup. Heat until the half & half is steaming and starting to bubble.
11) Remove from the microwave, and stir until the chips have melted and the icing is smooth.
12) Dip the top of each doughnut in the icing; or spread icing on the doughnuts.
Yield: 12 doughnuts.