Whisk the dry ingredients. Combine the flour, cocoa powder, baking powder, and salt in a medium bowl.
Mix the wet ingredients. Whisk together the melted butter and sugar. Add the eggs one at a time, then stir in the vanilla and espresso powder if using.
Make the dough. Fold the dry ingredients into the wet ingredients until a soft chocolate dough forms.
Chill. Cover and refrigerate the dough for at least 2 to 3 hours, or overnight for the easiest handling.
Prepare for baking. Heat the oven to 350°F (175°C) and line baking sheets with parchment paper.
Shape and coat. Scoop the dough into 1½ tablespoon portions. Roll into balls, then coat generously with powdered sugar. For brighter cracks, roll first in a little granulated sugar and then in powdered sugar.
Bake. Arrange the cookies about 2 inches apart and bake for 10–12 minutes, until the edges are set and the tops have crackled.
Cool. Leave the cookies on the baking sheet for 5 minutes before moving them to a wire rack to cool completely.