Sift together the flour, cocoa powder, baking powder, and salt in a bowl. Mix well to combine.
In a separate bowl, cream the butter, granulated sugar, and vanilla extract until light and fluffy. Add the eggs one at a time to the butter mixture, mixing well after each addition.
Gradually add the dry ingredients to the wet ingredients, one-third at a time, mixing until just combined. Avoid overmixing.
Cover the dough with plastic wrap, ensuring the wrap touches the dough, and chill in the refrigerator for 1 to 2 hours.
Preheat your oven to 170°C (340°F) and line a baking tray with parchment paper.
Scoop out 1 to 1.5 tablespoons of dough per cookie, roll into balls, and coat generously in powdered sugar.
Place the cookies on the prepared baking tray, spacing them out slightly. Gently press each ball down a bit if desired. Bake for 10-15 minutes or until the edges are set and the tops are cracked.
Allow the cookies to cool slightly on the tray before transferring to a wire rack to cool completely.