In a large bowl, sift together the flour, cocoa powder, baking powder and salt. Set the mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating between each addition, then add the vanilla extract and continue beating, scraping down the sides of the bowl as needed.
Add the flour mixture and beat until the dough is smooth. Divide the dough in half then roll each half in between two sheets of parchment paper or wax paper until they are about 1/4-inch thick. Slide the sheets of dough onto baking sheets (with the parchment paper) and refrigerate them for a minimum of 2 hours and up to overnight. (The refrigeration prevents the dough from spreading when baked, so don’t skip this step!)
Preheat the oven to 350°F.
Remove the sheets of dough from the fridge and use a cookie cutter to cut out shapes, arranging them about 2 inches apart on baking sheets lined with parchment paper. Bake the cookies for 10 to 12 minutes until they are firm around the edges. Remove the cookies from the oven and let them cool for 5 minutes on the baking sheets until you transfer them to a rack to cool completely. Decorate as desired with frosting and sprinkles or a dusting of confectioners' sugar.