Step 1In a glass bowl or measuring cup, combine the bittersweet chocolate and butter. Microwave, stirring every 30 seconds or so, until the chocolate and butter have melted and are combined. Set aside.
Step 2In a large bowl, sift together the flour, baking powder, baking soda, salt and cocoa. Set aside.
Step 3In the bowl of a stand mixer, or in a large bowl using a hand mixer, beat together the eggs, egg yolks and sugar until lightened in color, 2 to 3 minutes. Beat in the sour cream, vanilla and melted chocolate.
Step 4Gently beat half of the flour mixture, a spoonful at a time, into the egg mixture, then beat in the coffee. Continue to beat in the rest of the flour mixture, a spoonful at a time, until all of the ingredients are combined and a sticky dough is formed.
Step 5On a well-floured surface, roll the dough into a round just over one-half inch in thickness. Using a doughnut cutter, or 2 biscuit cutters (a larger one measuring 3 to 3 1/2 inches in diameter, and a smaller one measuring about 1 inch in diameter), cut the dough into doughnuts, spacing the doughnuts as close as possible. Collect the scraps and roll out to form another batch of doughnuts (note that this batch may be a little tougher than the first as the dough has been worked).
Step 6Fill a deep fryer with oil, or fill a large pot to a depth of at least 3 inches, and heat to a temperature of 350 degrees.
Step 7Gently place the doughnuts in the fryer, being careful not to crowd. Fry the doughnuts on each side until puffed and golden, about 4 minutes, flipping every 30 seconds or so.
Step 8Drain the doughnuts on a rack and cool slightly, then frost and decorate as desired.