Preheat the oven to 350°F (175°C).
In a large bowl, cream together the softened butter, granulated sugar, and powdered sugar until light and fluffy.
Add the egg, vanilla extract, and peppermint extract to the mixture, blending until well combined.
In a separate bowl, combine the flour, baking powder, and salt. Gradually add this to the wet mixture, stirring until just combined.
Fold in the crushed candy canes.
If desired, separate half of the dough and mix in red food coloring to create a contrasting color.
Scoop tablespoons of each color of dough and roll them together to form a swirl pattern.
Place the cookies on prepared baking sheets lined with parchment paper.
Bake in preheated oven for 10-12 minutes or until the edges are lightly golden.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to wire racks.
Enjoy your delicious candy cane cookies with friends and family!