Preheat oven to 350°F. Until you are to ready to assemble the cookies just prior to baking, keep the marshmallows in the freezer – otherwise they will thaw too rapidly.
In medium bowl combine flour, cocoa, and baking soda. Set aside.
Using an electric mixer, blend in butter with the granulated and brown sugar , scraping down the sides of the bowl. Add eggs and vanilla, and beat at medium speed until light and fluffy. Add the flour, cocoa, and baking soda and blend at low speed until combined. Batter will be very stiff. Fold in the Andes Peppermint Chips.
Using a 1 Tbls Cookie scoop, measure out one tablespoon of batter and flatten in the palm of your hand. Then place 4 marshmallows in the center of the dough disk and cover with another tablespoon of dough. Wrap the dough around the marshmallows, completely encasing them and forming a 2-inch-diameter dough ball.
Place balls on baking sheets lines with parchment or as silicon mat. Bake 15 minutes. Cool on pan 2 minutes, then transfer to a cool, flat surface.