In a large bowl, cream the shortening, butter and sugar until light and fluffy. Beat in the egg, milk and vanilla. Combine the flour, cocoa, baking powder, salt and cinnamon; gradually add to the creamed mixture. Cover and refrigerate for 8 hours or overnight.
On a lightly floured surface, roll dough to 1/8-in. thickness. Cut with a lightly floured-1/2-in. round cookie cutter; place on ungreased baking sheets.
Bake at 375° for 6-8 minutes or until set. Cool for 2 minutes before removing to wire racks to cool completely.
In a large bowl, combine all the peppermint layer ingredients. Knead for 1 minute or until smooth. Shape into 120 balls, 1/2 inches each. Place a ball on each cookie and flatten to cover cookie. Place on waxed paper-lined baking sheets; refrigerate for 30 minutes.
In a microwave, melt chips and shortening; stir until smooth. Spread about 1 teaspoonful over each cookie. Chill until firm. Yield: about 10 dozen.