In a large bowl, whisk together the flour, baking powder, and salt.

In a separate bowl, cream the softened butter and granulated sugar until light and fluffy, then beat in the egg and peppermint extract.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Chill the dough for at least 30 minutes if it's too sticky.

Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper.

On a lightly floured surface, roll out the chilled dough to about 1/4-inch thickness and cut into desired shapes using cookie cutters.

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

For the glaze, whisk powdered sugar and milk until smooth. Dip cooled cookies into the glaze or drizzle over them.

Immediately sprinkle with crushed peppermint candies before the glaze sets.