Beat butter and powdered sugar until light and fluffy, about 2 minutes.

Mix in flour and peppermint extract, then fold in crushed candy canes until evenly distributed.

Shape dough into a 2-inch log on plastic wrap, wrap tightly, and chill at least 30 minutes.

Preheat oven to 350°F. Slice log into ¼-inch rounds, place on parchment-lined sheets, and bake 12–14 minutes until edges are lightly golden.

Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.