Preheat your oven to 350°F (175°C).

Mix the butter and sugar together in a large bowl until creamy and light, about 3-5 minutes.

Add the eggs and vanilla extract, blending until fully incorporated.

Combine the flour, baking powder, and salt in a separate bowl. Gradually add this dry mixture to your wet ingredients, stirring gently until just combined.

Chill the dough in the refrigerator for at least 30 minutes.

Roll out the chilled dough on a floured surface to about 1/4 inch thick. Use a shamrock cookie cutter to create shapes.

Arrange the cookies on a parchment-lined baking sheet, leaving space between each one. Bake for about 10-12 minutes or until the edges are lightly golden.

Cool the cookies on a wire rack for at least 5 minutes before transferring them.

In a small bowl, whisk together powdered sugar and milk until smooth and drizzly. Adjust consistency if needed.

Decorate each cooled cookie with the green icing.