Whisk together the flour, cocoa powder, baking powder, and salt in a medium bowl.
Beat the butter and granulated sugar until light and fluffy.
Mix in the eggs one at a time, then add the vanilla extract.
Stir in the melted chocolate until fully combined.
Gradually add the dry ingredients and mix until a soft dough forms.
Cover and refrigerate the dough for at least 1 hour.
Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop tablespoon-sized portions of dough and roll generously in powdered sugar.
Arrange the dough balls on the prepared baking sheets about 2 inches apart.
Bake for 9–11 minutes until the tops are crackled and the centers remain soft.
Cool on the baking sheet for 5 minutes before transferring to a wire rack.