Heat the oven to 350°F. Grease two baking sheets. In a medium bowl, gently whisk together the flour, cocoa, baking powder, and salt. In a large bowl, mix the butter and sugar until creamy. Add the eggs, one at a time, and the vanilla, mixing well with each addition. Add the flour mixture and beat gently just until incorporated. Roll dough, a tablespoon at time, into balls, and roll each ball in powdered sugar until covered. Place balls about 2 inches apart on cookie sheets. Bake for 10-12 minutes, until tops puff and crinkle. Cool several minutes on cookie sheets before removing to a cooling rack.