Preheat the oven to 350 degrees Fahrenheit. Line two cookie sheets with parchment paper, or silicone liners, and set it aside.
Add the butter and sugar to a large mixing bowl (or the bowl of a stand mixer) and beat them together for about 2 minutes, until the mixture is light and creamy. 1 cup unsalted butter, 1 1/2 cups granulated sugar
Add in the egg, and yolk, vanilla extract, and peppermint extract and stir them into the mixture until combined. 1 large egg, 1 large egg yolk 1 tsp vanilla extract, 1/4 tsp peppermint extract
Add in the flour, candy cane pieces, baking powder, baking soda, and salt and stir it all together until you have a nice soft cookie dough. Scrape the bottom and sides of the bowl as needed. 3 cups all purpose flour, 1/2 cup crushed candy cane pieces, 1 tsp baking powder, 1/2 tsp baking soda, 1 tsp salt
Scoop the dough by 1.5 TBS portions and roll them into balls. Roll the balls in a small bowl full of additional granulated sugar. additional granulated sugar for rolling
Place the cookie dough balls at least 2 inches apart on the prepared baking sheets. Bake the cookies for 10 to 12 minutes, or until the tops are crinkled and the edges are just lightly golden.
Let the cookies cool for 5 minutes on the cookie sheet, then transfer them to a cooling rack to cool completely.