Preheat oven to 350°F (177°C).
In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars together on medium speed until light and fluffy, about 3 or 4 minutes. Scrape down the sides of the bowl and add the eggs, one at a time, beating well after each. Add the vanilla and beat again to incorporate.
Turn the mixer down to low and add the dry ingredients, mixing until just barely combined. Remove from the mixer and add in the chocolate chips and peanut butter chips, either with a spatula or by hand. I prefer to knead inclusions in by hand to ensure they're distributed evenly. Add the peanut butter and just fold it in gently. Don't mix it completely – you want to keep streaks and blobs of peanut butter throughout your dough.
Using a small cookie dough scoop or by forming the dough into small balls, portion the dough onto the baking sheets about 2 inches apart to allow for spreading. Press each down slightly with the palm of your hand.
Bake for about 16-18 minutes, rotating the baking sheet halfway through the baking time. Allow to cool on a wire rack for a few minutes before removing the cookies from the pan and allowing them to cool completely.