Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper. In a medium bowl, whisk together the flour, baking powder, and salt.

In a large bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the egg and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined and a dough forms. Do not overmix.

Roll out the dough on a lightly floured surface to about 1/4-inch thickness. Use cookie cutters to cut out desired shapes, then carefully transfer them to the prepared baking sheets.

Bake for 8-10 minutes, or until the edges are lightly golden. Let them cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

In a large bowl, beat the softened butter until creamy. Gradually add the powdered sugar, alternating with milk, until smooth and spreadable. Stir in the vanilla extract.

If desired, add a few drops of food coloring to achieve your preferred color. Once the cookies are completely cool, spread or pipe the frosting onto each cookie.