Cut the butter into roughly tablespoon size pieces and add to a microwave safe dish. Heat until melted or nearly melted, about 30 seconds. Set aside.
Place a fine mesh sieve over a large bowl. Measure the flour and add it to the sieve, shaking it gently back and forth into the bowl.
Measure the cocoa powder and add it to the sieve. Sift the cocoa powder into the flour. Set aside.
Add the paddle attachment to a stand mixer.
Place the sieve over the bowl of the stand mixture. Measure in the confectioners sugar and sift it into the bowl.
Add the melted butter into the confectioners sugar and mix on low until completely combined.
Add the vanilla extract to the butter and sugar and mix very briefly until combined.
Slowly pour the flour and cocoa into the butter and sugar. Mix on low speed until completely combined.
Place a sheet of parchment paper on your work surface. Put the shortbread cookie dough on top and cover with another piece of parchment paper. (Save this paper to line the cookie sheets.)
Roll out the dough to about 1/2 inch thick.
Place the rolled out dough and the parchment paper onto a sheet pan and place in the refrigerator. Let the dough chill for at least one hour. I often leave the dough in the fridge overnight, but I must then let it warm up slightly before I am able to use the cookie cutters.
Preheat the oven to 350 degrees Fahrenheit.
Leave the cookie dough on the bottom piece of parchment paper. Cut the dough into the desired shapes.
Place the top sheet of parchment paper on a baking sheet. Transfer the cut out cookies to the prepared pan. A spatula or a bench scraper can help you lift the dough up cleanly.
Bake until set, about 12-15 minutes. If you are using two pans, be sure to rotate them midway through the baking time.
Re-roll the remaining dough and cut out as many shapes as possible. If the dough becomes to warm, return it to the fridge for a few minutes.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool.