In a medium bowl, whisk together the cocoa, flour, baking powder, and salt. Set aside.
In the mixing bowl of a stand mixer, fitted with the paddle attachment, mix the butter and cream cheese on medium-high speed until smooth and creamy - about 2 minutes. Add the sugar and beat on medium-high speed until pale in color and fluffy. Next, add the egg and vanilla extract and mix on high speed until thoroughly combined. Scrape down the sides and bottom of the bowl as needed.
Turn the stand mixer to low, and slowly add the flour mixture until just combined. The dough will be sticky - this is ok.
Turn the dough out onto a sheet of plastic wrap, wrap tightly and chill it in the refrigerator for at least 2 hours, or overnight.
When the dough is chilled, adjust oven rack to middle position and preheat oven to 350o degrees. Line two baking sheets with parchment paper or silicone mats.
Lightly flour a work surface, or lightly flour the parchment paper or silicone mats used for the baking sheets. Rolling and cutting the dough on the liner of your baking sheets will make rolling, cutting and transferring the cookie dough cut-out much easier.
Roll the dough thick - about 3/8 inch thick. I keep a ruler handy whenever I roll out cookies to help with measuring the thickness.
You can lightly dust your cookie cutters with cocoa powder if necessary before cutting the dough. If you are cutting your cookies directly on your baking pan liners (the parchment paper or silicone mat), space your cuts leaving at least 1 inch between cookies. Also, cut the same size cookies on each baking pan so the cookies bake at the same time. If you mix large and small cookies, the smaller cookies will inevitably get over-baked.
You can use a small pastry brush to brush off any flour or extra cocoa powder off the cut-out cookies.
If your cookie dough and cut-outs are no longer chilled, place the dough and cut cookies back into the refrigerator for at least 10 minutes. It is important the dough is chilled when going into the oven to keep them from spreading too much and staying nice and thick.
Bake one baking sheet at a time. Bake the cookies until the edges are set and the centers are still soft but do not leave a fingerprint when lightly touched - about 10-11 minutes.
Allow the cookies to cool on the baking sheet for at least 5 minutes before transferring to a wire rack to cool completely.
Re-roll and cut remaining cookie dough. You will probably have a few scraps left, which can be discarded. Make sure the used baking sheets have cooled down before putting on the dough to bake the next batch. While you are waiting for your cookies and baking sheets to cool from the oven, this is a good time to stick the remaining cookie dough back into the refrigerator to keep chilled.
Make sure the cookies are completely cool before frosting and decorating.
Store the cookies in an airtight container and keep refrigerated (if using cream cheese frosting), for up to 1 week.