Beat butter, sugar, egg and vanilla in a large bowl (or the bowl of your stand mixer) until blended.
In a separate bowl, stir together flour, cocoa, baking powder, baking soda, and salt. Stir dry mixture into butter and sugar mixture, beating until well blended.
Refrigerate dough for an hour or so. On lightly floured board or between two pieces of wax paper, roll a small portion of dough at a time to 1/4-inch thickness.
Use a cookie cutter to cut into your favorite cookie cutter shapes.
Place cut out cookies on an ungreased baking sheet. I like to line mine with one of these. Cool slightly then remove to wire rack.
Heat oven to 325°F. Bake for five to seven minutes. Test for doneness by gently touching the top of a cookie. If no indentation remains, they're done. Cool slightly. Remove from cookie sheet to wire racks.