Start by making a half-batch of your favorite sugar cookie recipe. In a large mixing bowl, combine softened butter and sugar, beating until light and fluffy. Add 1 ½ teaspoons of peppermint extract and vanilla extract, mix until smooth.

Lightly flour a clean surface and roll the dough out to about ¼ inch thickness. Use a biscuit cutter to cut out small circles.

Preheat your oven to 350°F (175°C). Arrange the cut cookies on a baking sheet lined with parchment paper and bake for 3-4 minutes until edges are lightly golden.

Transfer cookies to a wire rack to cool completely for at least 10 minutes.

Prepare the Peppermint Buttercream Frosting by beating together softened butter, powdered sugar, and milk until smooth. Add peppermint extract and mix until fluffy.

Pipe a generous dollop of frosting onto each cookie using a decorating bag.

Sprinkle crushed candy canes over frosted cookies while the frosting is still soft.