Add the flour, cocoa powder, baking powder, and salt to a medium sized mixing bowl. Whisk to combine and set aside.
Add the softened butter and sugar to the bowl of a stand mixer, use the paddle attachment and beat on medium speed until fluffy, about 5 minutes.
Add the eggs and vanilla. Continue mixing until well blended.
Add the flour mixture a little at a time, and mix until combined.
Cover and chill for at least two hours (or up to 24 hours).
Preheat the oven to 375˚F. Line two cookie sheets with parchment paper.
Sift the powdered sugar into a small bowl so it is nice and fluffy.
Remove the cookie dough from the refrigerator.
Using a cookie scoop or spoon, scoop out about a heaping teaspoon of dough and shape into 1-inch sized balls.
Roll each ball in the powdered sugar to coat all sides, and place 2-inches apart on the prepared baking sheets.
Bake in a preheated oven until edges are set and tops are crinkled, about 8 to 10 minutes. Cool slightly, remove from baking sheet, and cool completely on a wire rack. Repeat with the remaining cookie dough.
Makes about 48 cookies.