Preheat oven to 375F. Place rack in middle position. Line two sheet pans with parchment paper.
Whisk together flour, baking powder, cocoa powder, and salt in medium bowl. Set aside.
In stand mixer, add butter and sugar and mix on high for 4-5 minutes, until light and fluffy.
Add in egg and vanilla, and continue mixing until smooth, scraping down sides of bowl as needed.
Decrease speed and add flour mixture in two additions. Mix until combined.
Divide dough into two pieces, cover with plastic wrap and chill in refrigerator for 1 1/2 - 2 hours.
Dust another sheet of parchment paper with flour, place one disc of dough and dust with a bit more flour, then roll out to ¼ inch thickness. Using cookie cutters, cut into desired shapes and place on prepared pans. Sprinkle sanding sugar on top.
Bake for 11-12 minutes.
Cool for 2-3 minutes on baking sheet. Then carefully remove and let fully cool on wire rack.