In a large bowl, beat together shortening, butter or margarine and sugar until light and fluffy. Add egg and peppermint extract; beat well.
Sift together flour, baking powder and salt; add to shortening mixture alternating with milk and mix well. Stir in oats; add in just enough food coloring to make a pink dough. Cover and chill for 1 hour.
Preheat oven to 375 degrees F (190 degrees C).
Roll out dough on a lightly floured board; cut out cookies with a floured 2 inch cookie cutter. Place on a lightly greased cookie sheet.
Bake in preheated oven for about 6 minutes. Remove cookies from sheet to cool.
Frost half of the cookies with frosting; top with remaining cookies, sandwich style.