2 1/2 cups powdered sugar
2 tablespoons water
1 tablespoon butter, softened
1 tablespoon light corn syrup
1/2 teaspoon vanilla or almond extract, if desired
Food color, if desired
Decorator candies, sugars, etc., if desired
Combine all cookie ingredients except flour in large mixer bowl. Beat at medium speed, scraping bowl often, until creamy (3 to 4 minutes). Reduce speed to low; add flour. Beat until well mixed (2 to 3 minutes).
Divide dough in half; wrap each half in plastic food wrap. Refrigerate until firm (at least 2 hours).
Preheat oven to 375°F.
Roll out dough on lightly floured surface, one-half at a time (keeping remaining dough refrigerated), to 1/4-inch thickness.
Cut rolled dough with a shamrock cookie cutter. Place cookies 1 inch apart onto ungreased cookie sheets. Bake for 7 to 10 minutes or until edges are very lightly browned. Cool completely.
Combine powdered sugar, water, 1 tablespoon butter, corn syrup and 1/2 teaspoon vanilla in small mixer bowl; beat at medium speed until powdered sugar is moistened (1 minute). Continue beating until mixture is smooth, adding additional water if necessary, to reach desired glazing consistency. Tint with food color, if desired. Glaze cooled cookies. Add decorator candies, if desired. Let stand until glaze hardens (6 hours or overnight).