Preheat oven to 350 degrees. Line a cookie sheet with parchment paper.
In a large mixing bowl, add the baking soda, salt, dry chocolate pudding mix, cocoa powder, and flour. Whisk until all of the dry ingredients are evenly distributed. Set aside.
In a separate large mixing bowl, add butter, peanut butter, brown sugar, and granulated sugar. Beat on medium with a hand mixer until light and fluffy.
Add in the egg and vanilla extract and beat until incorporated.
Add the dry ingredients into the butter mixture and beat on low until most of the dry ingredients are incorporated.
Add in 1 ¼ cups of peanut butter chips and beat on medium until the remaining dry ingredients are worked into the cookie dough.
Using a 2 T. cookie scoop, scoop the dough and make a large hole in the cookie while it's still in the scoop. Place a small square of chocolate into the hole and cover it with the dough that has been push over the sides of the scoop.
Roll the scooped cookie dough between your two palms applying light pressure until the dough is smooth.
Add back onto the prepared cookie sheet. Add a couple of peanut butter chips to the outside of the dough balls.
Place into the oven and bake for 12 minutes. Let cool for 5 minutes on the cookie sheet and transfer to wire rack to cool completely.