Preheat the oven to 350 degrees (F) and lightly grease a cookie sheet.
In a stand mixer or by hand with a beater, cream together the butter and the sugars for five minutes until smooth.
Add the egg, milk, and vanilla to the creamed mixture and combine.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt. Set the mixer on low and slowly add the dry ingredients, mixing until combined and a dough has formed.
Use a scoop or tablespoon to divide the dough into 15 cookies. Use your hands to roll each piece of dough into a smooth ball and place on the cookie sheet.
Using a sifter, sprinkle the cocoa powder evenly onto the cookies.
Bake for 13-15 minutes, or until cookies are firm in the middle and golden brown. Let cool for 5-10 minutes on the sheet, then move to a rack to cool.
Notes
If you want a sweeter cookie, mix 1/2 to 1 tablespoon of powdered sugar with the cocoa powder before sprinkling over the cookies.