Beat shortening and butter at medium speed with an electric mixer until creamy. Gradually add sugar, and beat until light and fluffy. Add eggs, milk, and vanilla extract, and beat until blended.
Combine flour, baking powder, and salt. Gradually add to shortening mixture, beating until smooth. Turn dough out onto a lightly floured surface.
Pat or roll dough to 1/4-inch thickness; cut 30 circles with a 1 3/4-inch round cutter. Reroll excess dough, and cut 30 circles with a 3 1/4-inch round cutter. Place dough circles on lightly greased baking sheets.
Bake at 350° for 11 to 14 minutes per batch or until lightly browned on edges. Cool 5 minutes; remove cookies to wire racks, and let cool completely.
Place a small dollop of Creamy Frosting in center of each large round cookie; top with 1 small round cookie. Divide remaining Creamy Frosting, and tint with desired food-coloring pastes. Spoon tinted icing into small zip-top plastic bags, and seal. Snip a tiny hole in 1 corner of each bag, and pipe desired decorative designs on cookies.