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