Whisk together flour, cocoa, baking powder, and salt in a medium bowl; set aside.
Cream butter, granulated sugar, and brown sugar in a large bowl until light and fluffy.
Beat in eggs one at a time, then add vanilla and melted chocolate until smooth.
Gradually fold the dry ingredients into the wet mixture until just combined; do not overmix.
Cover the dough and chill in the refrigerator for at least 1 hour (or up to 4 hours).
Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.
Scoop dough into 1.5-inch balls and roll generously in powdered sugar until fully coated.
Place 2 inches apart on the baking sheets and bake for 10–12 minutes.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
