01 - In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
02 - In a large bowl, beat the softened butter and granulated sugar together until light and fluffy, about 2 minutes.
03 - Add the egg and vanilla extract to the butter mixture and beat until combined.
04 - Gradually add the dry ingredients, mixing just until combined.
05 - Divide the dough into two discs, wrap in plastic wrap, and refrigerate for at least 1 hour.
06 - Preheat the oven to 350°F. Line two baking sheets with parchment paper.
07 - On a lightly floured surface, roll out one disc of dough to 1/4-inch thickness. Cut out shamrock shapes using a cookie cutter.
08 - Place cookies on prepared sheets 1 inch apart. Reroll scraps and repeat until all dough is used.
09 - Bake for 8–10 minutes, or until edges are just beginning to turn golden. Cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
10 - Whisk powdered sugar, 2 tablespoons milk, corn syrup, and vanilla until smooth. Add more milk if needed for a thick yet pourable consistency.
11 - Stir in green food coloring to reach desired shade.
12 - Decorate cooled cookies with green icing. Allow icing to set before serving.