Melt the dark chocolate in short bursts in the microwave; stir smooth and let it cool slightly.
Whisk flour, cocoa, espresso powder, baking powder, and salt in a medium bowl.
Beat granulated sugar and oil until sandy and combined. Add eggs one at a time, then mix in vanilla.
Stir in the melted chocolate and the cooled coffee until glossy.
Fold the dry ingredients into the wet just until a thick, sticky dough forms.
Cover and chill the dough until firm enough to scoop, 1 to 2 hours.
Heat oven to 350°F. Line two baking sheets with parchment. Place the coating sugars in separate bowls.
Scoop 1½-tablespoon portions, roll into balls, coat in granulated sugar, then heavily in powdered sugar.
Arrange 2 inches apart and bake 10 to 12 minutes, until cracked and just set in the centers.
Cool on the sheet for 5 minutes, then move to a rack to finish cooling.