On a large clean working surface, line the chocolate wafers into pairs, matched by size. In a large mixing bowl, cream together the butter and shortening until light and fluffy. Gradually add in the powdered sugar, alternating with a Tablespoon of the milk at a time. Beat in the vanilla. Continue to mix on medium-high speed until the cream is light and fluffy. Add more milk if the filling is too thick, add more sugar if the filling is too thin.
Fill a pastry bag fitted with a large round tip. Pipe the icing onto one cookie per each pair, top with the other cookie.