Sift together flour, cocoa powder, baking soda and salt. Set aside.
In a stand mixer fitted with a paddle attachment or a large mixing bowl with electric hand mixer, cream butter with sugars. Add egg and vanilla. Blend until smooth.
Slowly add dry mixture to wet mixture. , will be dark and thick.
By hand, fold in peanut butter chips. If you do this with the electric mixer, the chips with break into smaller pieces because the dough is so dense.
Divide dough in half. Form each half into a log about 1 1/2 inches in diameter. Roll in plastic wrap and refrigerate for at least an hour.
Preheat oven to 350 degrees. Remove cookie dough from plastic wrap and slice into 1/2 inch thick medallions. Place on am insulted cookie sheet lined with parchment paper.
Bake for 10 minutes. They might look slightly undercooked, but will harden up while cooling.
Allow to cool for 5 minutes before removing to a cooling rack. Repeat with remaining dough.
Allow cookies to fully cool.
For Creamy Peanut Butter Frosting:
In a stand mixer fitted with a paddle attachment or a large mixing bowl with electric hand mixer whip butter until pale and fluffy. Add peanut butter, incorporating fully.
Add powdered sugar. Mixture will be dry and grainy.
Add milk and vanilla, beating until smooth.
Place heaping tablespoons of creamy peanut butter frosting on the inside of one cookie and top with another to form a cookie sandwich.
If you've tried this recipe, come back and let us know how it was!