Preheat oven to 350°F. Line your baking sheets with parchment paper. While you can use a silicone mat if you like, the cookies tend to stick a bit more.
Melt the butter, then mix in the cocoa powder until smooth.
In a bowl, mix together the flour, sugars, baking powder, and salt.
Stir the eggs and vanilla into the butter mixture.
Add the wet ingredients to the dry and beat together until combined well.
Roll the dough into roughly one tablespoon balls. Roll those balls in powdered sugar to coat them.
Place the dough balls on your baking sheets, about 3" apart, to give them space to spread.
Bake for 11-13 minutes. They may look a little under-done; that's fine, they're a soft cookie.
Let cool, transferring to a cooling rack if you want. Then enjoy!