In a medium bowl, whisk together flour, baking soda, and salt. Set aside.In a large bowl, beat softened butter, granulated sugar, and brown sugar until light and fluffy.Add egg, peppermint extract, and vanilla extract. Beat until well combined.Gradually mix dry ingredients into wet ingredients until just combined.Gently fold in ¼ cup of finely crushed peppermint candy canes.Cover dough and refrigerate for at least 1 hour (or up to 24 hours).Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.Place powdered sugar in a small bowl. Place additional granulated sugar in another small bowl.Scoop chilled dough (about 1 tablespoon each). Roll first in granulated sugar, then generously coat in powdered sugar.Place 2 inches apart on prepared baking sheets.Bake for 9-11 minutes, until edges are set but centers remain soft.Immediately upon removing from oven, gently sprinkle remaining crushed peppermint on top.Let cool on baking sheet for 5 minutes, then transfer to wire rack.
