Prepare the baking sheet:
Line a cookie sheet with parchment paper or a silicone baking mat and set aside.
Sift the dry ingredients:
In a medium bowl, sift together the flour, cocoa powder, baking powder, and baking soda. Set this aside for later.
Set aside rolling sugar:
Reserve ½ cup of sugar to roll the cookie dough balls in before baking.
Cream the butter and peanut butter:
Using a stand mixer or hand mixer, cream together the softened butter and peanut butter until well combined and smooth.
Add sugars:
Add the light brown sugar and remaining sugar to the butter mixture. Cream together until light and fluffy.
Add eggs and vanilla:
Beat in the eggs one at a time, mixing until just combined. Add the vanilla extract and mix well.
Combine wet and dry ingredients:
Gradually add the sifted dry ingredients to the wet mixture. Mix on low speed until the flour is fully incorporated, being careful not to overmix.
Chill the dough:
Cover the cookie dough and refrigerate for 1 hour.
Preheat the oven:
Preheat your oven to 350°F (175°C).
Form the dough balls:
Scoop out the dough using a small cookie scoop or tablespoon, shaping them into 1 to 1½-inch balls.
Roll in sugar and press:
Roll each dough ball in the reserved ½ cup of sugar until fully coated. Place them on the prepared baking sheet about 2 inches apart. Using a fork, press a criss-cross pattern onto each cookie. To prevent sticking, dip the fork in sugar before pressing.
Bake:
Bake the cookies for 8-10 minutes, or until the edges are set.
Cool the cookies:
Allow the cookies to rest on the baking sheet for 2-3 minutes before transferring them to a cooling rack to cool completely.
Store:
Once cooled, store the cookies in an airtight container for up to a week.