In the large bowl of an electric mixer, combine the butter and sugar and beat on medium speed until light and fluffy. Beat in the egg yolk, and then the whole egg and vanilla.
In a medium bowl, sift together the flour, cocoa, baking powder and salt. Add flour mixture to batter. Beat on low just until combined. Divide the dough in half. Flatten each portion into a disc, wrap tightly in plastic and chill for at least 1 hour. (You can refrigerate the dough for up to 2 days or freeze for up to 1 month.)
Preheat oven to 350 F. Line baking sheet with baking liner or parchment paper. Turn dough out onto a lightly floured surface and roll out to 1/8" thickness. Using cookie cutters, cut out cookies. Transfer cookies to baking sheets, spacing them about 1/2" apart. Gather dough scraps, reroll and cut out more cookies. At this point, sprinkle cookies with decorating sugars. Bake cookies until golden brown around edges, about 8 to 10 minutes. Transfer to wire racks to cool. If desired, decorate completely cooled cookies with decorative icing.
Makes about 48 3" cookies.