In a large bowl, sift together flour, cocoa powder, baking powder and salt. Whisk to combine.
In another large bowl with a hand mixer or in the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar on high speed until fluffy.
Add the egg and vanilla extract and mix on high speed until just combined. Scrape down the sides of the bowl as needed.
Gradually add the flour mixture to the butter mixture and mix on low speed until combined. I like to do this in 3 batches.
Place dough on a flat surface and divide in half. Shape each half into a 9 inch long and 1 1/2 inch diameter log.
Wrap each log tightly in plastic wrap. Place in refrigerator to chill for at least 1 hour.
Once dough has chilled through, preheat oven to 350°F and line two baking sheets with parchment paper.
Using a very sharp knife, slice the logs into thick slices and place on baking sheet. You can place them fairly close as the cookies will not spread much.
Bake for 10 minutes and then remove from the oven. Cool on baking rack.