In a large bowl, cream together the butter and sugar until somewhat fluffy. Then beat in the vanilla until well blended.
Slowly add cornstarch and flour.
Cover with plastic wrap and place in refrigerator for an hour.
Preheat oven to 350.
When the batter is firm, form into 1 inch balls and the hand roll them out into cylinder shapes and make a horse shoe shape.
Dip each cookie into the coconut. The coconut is sticky, so it will adhere to the cookie with no problem.
Bake for approximately 10 - 12 minutes, or until lightly golden brown.
Allow to cool on cookie sheet before transferring to cooling rack