Beat on low, powdered sugar and softened butter. Mix until powdered sugar is incorporated.
Continue beating on medium-high speed. Scrap sides and bottom of bowl often. When completely mixed together the frosting may appear dry.
Add milk, a little bit at a time until frosting is the proper consistency. Add peppermint extract, mix well.
Fit decorating bag with decorating tip. Spoon mint buttercream frosting into decorating bag. Pipe mint buttercream frosting on flat side of one cookies. Place second cookie, flat side down, on top of mint buttercream frosting. Set aside and continue with remaining cookies.
Preheat oven to 325°
Combine flour, cocoa, baking soda, and salt in small bowl. Beat butter, sugar, brown sugar and vanilla extract in large mixer bowl until creamy. Add eggs, one at a time, beating well after each addition. Gradually beat in flour mixture. Stir in morsels. Drop by well rounded tablespoon onto un-greased baking sheets.
Bake for 11 to 13 minutes or until cookies are puffed and centers are set. Cool on baking sheets for 2 minute; remove to wire racks to cool completely.