Preheat oven to 350°F. Line two baking sheets with parchment paper.
Put the confectioners' sugar into a bowl and set aside.
In a medium bowl, stir together the flour, cocoa, baking powder and salt. Set aside.
In a large bowl, using an electric mixer, beat the butter and sugar on medium speed until creamy, about 3 minutes. Turn off the mixer and scrape down the bowl with a rubber spatula. Add 1 egg and beat on medium speed until blended. Add the other egg and vanilla and beat until blended.
Turn off the mixer and add the flour mixture. Beat on low speed just until blended.
Using a tablespoon, scoop up a rounded spoonful of dough. Scrape the dough off the spoon into the palm of your other hand. Roll the dough into a ball. Roll the ball in the confectioners' sugar until covered. Place the balls on a prepared baking sheet. Repeat, spacing the balls about 2 inches apart.
When 1 baking sheet is full, put it in the oven and bake the cookies until they are crackled and puffed, 10 to 12 minutes. Using oven mitts, remove the baking sheet from the oven and set it on a wire rack for 15 minutes.
Place the cookies onto the rack and let cool completely. Repeat with the rest of the cookies. Makes about 24 cookies.