Combine all ingredients in the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl. Mix on low speed until the mixture forms a cookie dough, scraping the bowl occasionally.

Divide the dough in half. Place each half between sheets of waxed paper and roll out to about 1/4 inch thickness. Chill in the refrigerator for at least 30 minutes.

Preheat the oven to 375°F. Cut out cookies into shamrock shapes or your preferred shapes and place them on a parchment-lined baking sheet.

Bake for 6-10 minutes or until the edges are just starting to brown. Let cookies cool completely before decorating.

For the frosting, beat softened butter until smooth, then gradually add powdered sugar, vanilla extract, and milk until reaching desired consistency. Tint the frosting green with food coloring.

Frost the cooled cookies with green frosting and decorate with green sanding sugar. Allow frosting to set.