Preheat your oven to 375 degrees F. Line a baking sheet with parchment paper. Set aside.
Combine the all-purpose flour, cake flour, cocoa powder, baking powder, salt, and baking soda in a medium sized bowl. Whisk together. Set aside.
In a stand mixer fitted with the paddle attachment, combine the cold butter and sugars and beat on medium speed until light and fluffy, about 2 minutes.
Add the whole egg and egg yolk and mix until combined. Scrape down the sides of the bowl and mix again for about 30 more seconds.
Turn the mixer on low speed and add the dry ingredients in three separate additions, only mixing until the dry ingredients are incorporated.
Stir in the peanut butter chips.
Measure 5.75 oz. of cookie dough and shape into balls. Place 4 cookie dough balls on the baking sheet and bake for 11 minutes.
Let the cookies cool for about 10 minutes and then serve while still warm. To eat later, heat a cookie in the microwave for about 15-20 seconds.
*Please don't use any other brand but Reese's! I've tried every peanut butter baking chip out there and these are simply the best. They make a huge difference to the flavor of the cookie and any other peanut butter chip just wouldn't be the same.
**This is about a bag and a half.