Preheat the oven to 350°F (175°C).
In a bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, cream the softened butter, granulated sugar, and powdered sugar until light and fluffy.
Add the egg, vanilla extract, and peppermint extract to the creamed butter mixture, beating until well incorporated.
Gradually add the dry mixture to the creamed mixture until just incorporated.
Fold in the crushed candy canes gently to avoid breaking them down too much.
Scoop the dough onto lined baking sheets, keeping them spaced out.
Bake in the preheated oven for 10-12 minutes until the edges are golden and the centers are set.
Allow the cookies to cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely.
Once cooled, garnish with additional crushed candy canes for decoration, if desired.