In a medium-sized bowl whisk together the flour, cake flour, cocoa, baking powder, baking soda and salt.
In a large bowl beat together the butter, brown sugar, and white sugar until fluffy.
Beat in the eggs and vanilla extract.
Turn the mixer down to low speed and beat in the flour mixture about ½ at a time. The batter will be very thick.
Stir in the chocolate chips.
Form the dough into balls using about ¼ to ⅓ cup per cookie (I use a cookie scoop), and place 3 inches apart on lined cookie sheets. Flatten the cookies slightly.
Cover the cookie sheets with plastic wrap and refrigerate for 1 hour, or overnight.
When ready to bake, preheat the oven to 375F degrees.
Remove the plastic wrap from the cookie sheets, and bake the cookies 1 tray at a time on the middle rack of the oven for 13-15 minutes, or until the tops look just set.
Remove from the oven and place a few peanut butter chips on the top of each cookie. Allow the cookies to cool on the tray for at least 5 minutes, then transfer to a wire rack and continue cooling.