In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt; set aside.
Using an electric mixer fitted with the whisk attachment, combine the brown sugar, eggs, espresso powder, and vanilla extract. Beat on medium-high speed until well-combined, 2-3 minutes.
Break the unsweetened chocolate up into pieces and combine with the butter in either a microwave-safe bowl, or a heatproof bowl set over simmering water. If using the microwave, warm chocolate and butter at 50% power in 30 second intervals, stirring in between each; if using the stovetop, stir chocolate and butter frequently while it melts over the simmering water. The chocolate and butter should fully melt into a smooth mixture.
Pour the melted chocolate into the mixer bowl and whisk it into the sugar-egg mixture until fully incorporated. Using a rubber spatula, fold in the dry ingredients until no streaks of flour remain. Let the dough sit at room temperature for 15-20 minutes.
Preheat oven to 325 degrees F and set a rack in the center of the oven. Line baking sheets with silicone baking mats or parchment paper.
Place the granulated and powdered sugars in separate shallow dishes. After the dough has rested, scoop out dough balls of approximately 1 and 1/2 tablespoons each. Dampen your hands slightly to help roll them into smooth balls. (I found it works well to run my hands under the faucet, shake them out quickly, roll about six balls, and repeat.) Roll each ball first in the granulated sugar, then the powdered sugar, and space them evenly on the prepared baking sheets.
Bake one sheet at a time for about 12 minutes, rotating the pan 180 degrees halfway through the baking time, until the cookies are puffed up and crackled. Transfer the pans to wire racks and allow the cookies to cool completely on the pans before serving or storing.
Notes
Storage:Cookies keep well at room temperature for 4-5 days.
Recipe: Adapted from Smells Like Home, originally from Cook’s Illustrated, November/December 2014.