In a mixing bowl, cream butter and sugar. Add egg and vanilla; mix well. Combine the flour, cocoa, baking powder, baking soda and salt; add to creamed mixture alternately with milk. Shape into two 10-1/2-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 sheets. Bake at 325 degrees F for 9-11 minutes or until edges are set. Remove to wire racks to cool. Combine filling ingredients; beat until smooth. Add food coloring if desired. Spread on the bottom of half of the cookies; top with remaining cookies.