In a stand mixer, using a paddle attachment, beat butter with sugar on high speed for about 5 minutes until the mixture is fluffy and pale in color.
Add an egg (room temperature) and vanilla extract and beat again until well combined.
Scrap the sides and the bottom of the mixing bowl with a spatula to make sure everything is well mixed.
Mix flour, cocoa powder, baking powder, and salt together in a separate bowl, then add to the wet ingredients in two steps. Mix in between on low speed until all combined but try not to overmix.
Slightly knead the dough with hands, making a ball/disk shape, and wrap it in the plastic wrap. Refrigerate for 1-2 hours or overnight.
When ready to bake, take the dough out from refrigerator and let it sit on the counter for 10 minutes.
To roll out the dough, put the dough between two sheets of parchment paper, then roll over the parchment paper. The paper will keep the dough smooth and will not stick.
After you cut out the cookies and put them on the baking sheet, put the sheet with the cookies back in the fridge for 10 minutes to chill. Chilled dough will help your cookies to keep their shape.
Bake cookies for about 9-10 minutes at 350°F. When you take them out of the oven, let them sit on the baking sheet for about 10 minutes, then transfer to a wire rack.