Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy. Add the vanilla extract and egg, and mix well.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
If desired, add a few drops of green food coloring to the dough and mix until the color is evenly distributed.
Roll out the dough on a floured surface to about 1/4 inch thickness. Use a shamrock-shaped cookie cutter to cut out cookies and place them on the prepared baking sheet.
Bake in the preheated oven for 8-10 minutes, or until the edges are set but not browned.
Allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.