Beat butter and sugar in a large bowl with an electric mixer for 3 minutes on medium high. Add egg, milk and flavoring. Beat on medium for 20 seconds.
Turn mixer to low and gradually add flour. Place as much cookie dough as you can in cookie press with shamrock shaped attachment. Press cookies onto greased cookie sheet or a cookie sheet lined with a silicone mat. Add green sugar and piece of candy for stem.
Bake at 375°F for 8-10 minutes. (Note: Check the cookies at 8 minutes. They might be done already and you don't want the candy to brown.) Let cool and serve. Store covered for a few days or you can freeze them for several weeks in an airtight container.