In a mixing bowl, cream butter and sugar. Beat in egg and extracts. Combine flour, baking soda and cream of tartar; gradually add to the creamed mixture. Divide dough in half; stir chocolate into one half. Refrigerate for 2 hours or until easy to handle. On a lightly floured surface, roll out each portion to 18-in. thickness. Cut with a 2-1/2-in. cookie cutter. Place 1 in. apart on lightly greased baking sheets. Bake at 375 degrees F for 7-8 minutes or until lightly browned. Remove to wire racks to cool.
For frosting, combine sugar, extract, salt and enough milk to achieve spreading consistency. Add food coloring if desired. Frost chocolate cookies. Place a wooden stick on each cookie, leaving 3 in. for handle. Top each with a plain cookie. Frost tops.