In a mixer, cream together the butter and sugar until light and fluffy. Beat in egg, milk and vanilla. Combine flour, baking cocoa, baking powder, baking soda and salt. Stir into the creamed mixture.

Divide the dough in half and shape into two ten inch rolls. Wrap in plastic wrap and refrigerate an hour or overnight.

Preheat oven to 325 degrees. Line a cookie sheet with parchment paper.

Unwrap dough and slice into 1/8 inch slices and place on prepared baking sheets.

Bake for 9 to 11 minutes until edges are set. Remove to wire racks to cool completely.

Whisk together all frosting ingredients. Place into a plastic Ziploc bag and cut off a small piece of the corner. Squeeze frosting onto half of the cookies. Top with the remaining cookies.