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 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° for 9-11 minutes or until edges are set. Remove to wire racks to cool.
In a small bowl, combine confectioners' sugar, butter, milk extract and if desired red food coloring; beat until smooth. Spread on the bottoms of half of the cookies; top with remaining cookies.
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