In a medium mixing bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder and salt.
In a large mixing bowl, use a hand mixer or the paddle attachment of a stand mixer to beat together the butter and granulated sugar on medium speed until creamy.
Add the eggs and vanilla and mix on medium speed until well combined, scraping down the sides of the bowl as needed.
Mix in the flour and cocoa powder mixture on low speed, until combined. The dough will be fairly soft and sticky.
Cover the bowl and chill the dough for at least 3 hours and up to 2 days.
When you are ready to bake the cookies, preheat the oven to 350° F. Line baking sheets with parchment paper.
Place the powdered sugar in a wide shallow bowl or pie dish. Roll the cookie dough into 1-inch balls and then roll the balls in the powdered sugar until fully coated. Place on the prepared baking sheet, about 2 inches apart.
Bake for 9-11 minutes, until cookies are just set and almost no indentation remains when you gently touch a cookie in the center. Let cookies cool on the baking sheet for 5 minutes and then transfer to a wire rack to finish cooling.