Method:
In a medium bowl, whisk together flour, baking powder and kosher salt.

In a separate bowl or the bowl of a stand mixer, whip butter on high speed until soft and fluffy.

Mix in the granulated sugar, followed by the egg, vanilla extract, and gel food coloring.

Add the dry ingredients and mix on low until just combined. Do not overmix.

Flatten into a disc. Wrap in clingfilm/plastic wrap and refrigerate until firm, at least 4 hours, or overnight.

Line a half-sheet rimmed baking tray with parchment or a silicone mat. Set aside.

Unwrap dough and allow to sit at room temperature for 5-10 minutes, or until just soft enough to roll. On a floured countertop or silicone rolling mat, use a rolling pin to roll the chilled dough to 1/4-inch thickness.

With a 2 1/2-inch shamrock cutter, cut the dough into shamrocks. Re-roll scraps and repeat with remaining cookie dough.

Arrange on prepared tray.

Refrigerate tray for 30 minutes, or freeze for 15 minutes, or until cookies are cold and firm to the touch. Meanwhile, preheat oven to 350° F / 176° C.

Bake in preheated oven for 12-14 minutes, or until very lightly golden brown around the edges. Do not overbake.

With a metal spatula, transfer cookies to a wire rack to cool. Meanwhile, prepare the buttercream.

Buttercream:

In a large mixing bowl or the bowl of a stand mixer, whip butter on high speed until light and fluffy.

Add the confectioner’s sugar in small increments, alternating with the milk and mixing after each addition.

Add the peppermint oil and mix until smooth and creamy, about 3-5 minutes. If necessary, add more confectioner’s sugar or milk to adjust the consistency. The buttercream should be thick and creamy, but soft enough to pipe.

Mix in the gel food coloring.

Add the buttercream to a piping bag fitted with a 1/4-inch star tip.

Pipe as desired.

Decorate with shamrock sprinkles.

Store leftover cookies in an airtight container at room temperature for up to 3 days.