Sift together the flour, cocoa, baking powder and salt; set aside. In a medium bowl, cream together the butter and sugar until smooth. Beat in the egg. Gradually stir in the sifted ingredients to form a soft dough. Divide dough into 2 pieces, flatten and wrap in plastic wrap. Refrigerate for 2 hours.
Preheat the oven to 375 degrees F (190 degrees C). On a lightly floured surface, roll the dough out to 1/8 inch in thickness. Cut into desired shapes with cookie cutters. Dough is sticky so be sure to add more flour to the rolling surface as needed. Place cookies 1 1/2 inches apart onto cookie sheets.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.
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