Prepare the Cookie Dough:

• In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
• In a larger bowl, using a hand mixer or stand mixer fitted with a paddle attachment, beat the softened unsalted butter and granulated sugar together on high speed until creamy and smooth.
• Add the large egg, pure vanilla extract, and the seeds from 1 vanilla bean to the butter-sugar mixture. Beat on high speed until fully combined.
• Gradually add the dry ingredients to the wet ingredients, mixing on low speed until combined. The dough will be relatively soft.

Chill the Dough:

• Divide the dough into two equal portions.
• Place each portion onto a piece of lightly floured parchment paper or silicone baking mat.
• With a lightly floured rolling pin, roll out each portion to about 1/4-inch thickness.
• Stack the rolled-out dough (with parchment paper or baking mats) onto a baking sheet and refrigerate for at least 1–2 hours or until firm.

Cut and Bake:

• Once the dough is firm, preheat the oven to 350°F (177°C).
• Line baking sheets with parchment paper or silicone baking mats.
• Using shamrock-shaped cookie cutters (or any desired shape), cut the dough into cookies and place them onto the prepared baking sheets, spacing them about 2 inches apart.
• Re-roll any leftover dough and continue cutting until all dough is used.
• Bake the cookies for 11–12 minutes or until the edges are lightly browned.
• Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.

Prepare the Vanilla Bean Buttercream:

• In a medium bowl, using a hand mixer or stand mixer fitted with a paddle attachment, beat the softened unsalted butter on high speed until creamy.
• Gradually add the confectioners’ sugar, heavy cream, pure vanilla extract, and the seeds from 1 vanilla bean. Beat on low speed until combined, then increase to high speed and beat for 3 full minutes.
• If desired, add a pinch of salt to taste and green food coloring to achieve the desired shade.

Decorate the Cookies:

• Once the cookies have cooled completely, spread or pipe the vanilla bean buttercream onto each cookie.
• Decorate with sprinkles if desired.
• Allow the decorated cookies to set at room temperature for a few hours before serving or storing.