Preheat the oven to 375 degrees F. Line several baking sheets with parchment paper and set aside. In a medium bowl, mix the flour, cocoa powder, baking powder, and salt.
In the bowl of an electric stand mixer, combine the softened butter and sugar. Cream the butter and sugar together on high speed until light and fluffy, 3-5 minutes. (This breaks down the sugar crystals; don’t skip!) Then turn the mixer on low and add in the eggs and vanilla extract. Once combined, turn off the mixer and scrape the bowl with a rubber spatula.
Turn the mixer on low, and slowly add the flour mixture. Scrape the bowl and beat again for 30 seconds. Do not over-mix.
Pour some extra sugar into a bowl to coat the cookies. Portion the dough into heaping tablespoons and roll into 1 inch balls. The dough should be soft and delicate - Don't over-handle. Shake each ball in the sugar bowl to coat. Then place the balls on the cookie sheets 2 inches apart. Use the bottom of a drinking glass to press each ball, until it's 1/2 inch thick.
Bake each sheet of sugar cookies for 9-11 minutes, until the edges are slightly golden and the centers are just barely set. Cool completely on the cookie sheets.
These cookies are somewhat thin and soft. If you would like thicker puffier cookies, chill the dough for at least 1 hour before rolling into balls. Make sure to work fast so the dough is still cool when it goes into the oven. Bake for 11-14 minutes.If you want to turn these delicate cookies into cut-out cookies: Use 3 1/4 cups flour and 3/4 cup cocoa powder. Make sure to chill the dough before rolling and cutting.