Preheat oven to 350 degrees F (175 degrees C). Lightly grease baking sheet.
Cream together the butter or margarine and the pudding mix. Blend in the baking mix, egg and sugar and mix well.
On a lightly floured surface roll out the dough to 3/8 inch thickness and cut into cookies with a shamrock cookie cutter.
Place cookies on the prepared baking sheet and bake at 350 degrees F (175 degrees C) for 9 to 10 minutes or until lightly browned on the edges. Let cookies cool on rack. Frost with green colored icing if desired.