In a medium bowl, whisk together flour, baking powder, and salt until combined. Set aside.
Use a double boiler (or, stack a small pan into a large pot of boiling water, making sure the bottom of the small pan doesn't touch the bottom of the large pan) and heat until both the butter and chocolate melts. Make sure you stir constantly so that the chocolate doesn't burn. Set aside to cool slightly.
Use a freestanding electric mixer with a paddle attachment (or handheld whisk) to beat together the sugar, eggs, vanilla, and espresso powder on medium-high speed for at least five minutes.
When the sugar/eggs/vanilla/espresso mixture is ready, lower your mixer speed to the lowest setting and stir in the chocolate/butter mixture (from the second step).
Once the two mixtures have been incorporated, add the flour/baking powder/salt mixture from the first step. Beat until just combined -- do NOT overbeat or you will get tough cookies and I will cry. There should be one or two flour streaks left in the mixture.
Chill the dough for 2 to 3 hours. Once the dough has been chilled, it should have the consistency of Playdough.
When the dough is ready and chilled, preheat the oven to 325 (F).
Put a cup of confectioners' sugar into a shallow bowl, preferably a large tupperware with a lid. Using a tablespoon-sized cookie scoop, scoop out tablespoon-sized portions of the dough and use your hands to roll it into a ball:
They should be roughly 1 1/4 inches in diameter.
Drop the dough balls into the confectioners' sugar as you go. Once about five or six are in the bowl (I used 3 or 4 since my tupperware was smaller), cover the tupperware with a lid and shake and toss the bowl to coat the balls with the sugar. Be careful not to do this with too many balls at a time, since they have a tendency to stick together!
Place the coated dough balls on a lightly greased or parchment-lined cookie sheet, leaving about 1 1/2 inches between them. Bake the cookies in a preheated oven for 10 - 12 minutes. As the cookies bake, they'll flatten out a little bit and acquire their distinctive "cracked" appearance. Remove the cookies from the oven, letting them rest on the baking pan for a few minutes before turning out into a wire rack to cool completely.