Preheat an oven to 350°F with the racks in the middle. Grease 2 baking sheets with butter.
Put the confectioners' sugar into a bowl and set aside.
In another bowl, using a wooden spoon, 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 the prepared baking sheets. Repeat, spacing the balls about 2 inches apart.
Put the cookies in the oven and bake until they are crackled and puffed, 10 to 12 minutes. Using oven mitts, remove the baking sheets from the oven. When the cookies have cooled a few minutes, use a firm spatula & transfer the cookies onto the rack and let cool completely. Repeat with the rest of the cookies.