1. In a Large Bowl, Cream butter and sugar until light and fluffy. Beat in egg and vanilla. Combine the flour,cocoa, baking powder, baking soda and salt; gradually add to creamed mixture alternately with milk, beating well after each addition. Shape into two 101/2-in rolls; wrap each in plastic wrap. Refrigerate overnight.
Unwrap dough and cut into 1/8-in. Slices.
Place 2 in. Apart on lightly greased baking sheet. Bake at 325 for 9-11 minutes or until edges are set. Remove to wire racks to cool.
3. In a small bowl,combine confectioners sugar, butter, milk, peppermint extract, and, if desired, food colouring; beat until smooth. Spread on the bottoms of half of the cookies; top with the remaining cookies.