Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a mixing bowl, sift together the all-purpose flour, baking powder, and salt. Set aside.

In another large bowl, use an electric mixer to cream the softened butter and granulated sugar together until light and fluffy.

Beat in the egg, vanilla extract, and peppermint extract until well combined.

Gradually add the flour mixture to the wet ingredients, mixing until just incorporated. Fold in the crushed peppermint candies.

Roll out the cookie dough on a floured surface to about ¼ inch thick. Use cookie cutters to cut out desired shapes and place them on the prepared baking sheet.

Bake in the preheated oven for 10-12 minutes or until the edges are lightly golden. Remove from the oven and let cool on the sheet for a few minutes before transferring to a cooling rack.

While the cookies are cooling, prepare the frosting by whisking together the powdered sugar and milk until smooth. Adjust the consistency by adding more powdered sugar or milk if necessary.

Once the cookies are completely cooled, drizzle or spread the frosting over each cookie and sprinkle with additional crushed peppermint candies.