1. Preheat the oven to 350°F and line two baking sheets with parchment paper.

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

3. In a large bowl, beat 1 cup softened butter with the granulated sugar until light and fluffy.

4. Add the egg and vanilla extract, then mix until smooth.

5. Gradually add the dry ingredients and mix just until a soft dough forms.

6. Scoop the dough into even portions, roll lightly, and place them on the prepared baking sheets about 2 inches apart.

7. Gently flatten each dough ball slightly, then bake for 9 to 11 minutes until the edges are just set.

8. Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.

9. For the frosting, beat the cream cheese and 1/4 cup softened butter until smooth.

10. Add the powdered sugar, peppermint extract, and pink food coloring, then beat until fluffy and spreadable.

11. Spread frosting over each cooled cookie.

12. Sprinkle crushed candy canes on top and let the frosting set before serving.