Preheat oven to 350°F (175°C) and line two baking sheets with parchment. Cream the butter and 3/4 cup sugar until light and fluffy, about 2 minutes.

Beat in the egg and peppermint extract, then mix in the flour, baking powder, and salt just until combined.

Combine the crushed candy canes and 2 tablespoons sugar in a small bowl. Scoop tablespoon sized dough balls, roll into rounds, then coat in the candy mixture.

Place 2 inches apart on the baking sheets and bake 10 to 12 minutes, until edges are set and tops look dry.

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