In a mixing bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set this mixture aside.

In the bowl of an electric stand mixer fitted with the paddle attachment, cream together the unsalted butter, granulated sugar, and brown sugar until smooth, scraping down the sides of the bowl periodically.

Mix in the egg and then add the egg yolk. Blend in the vanilla extract and peppermint extract, ensuring everything is well combined.

Slowly add the flour mixture to the wet ingredients, mixing just until combined. Be careful not to over-mix.

Pour in the white chocolate chips and crushed candy canes. Gently mix to combine.

Using a #40 cookie scoop, scoop out the dough and shape into balls. Place them on a tray lined with parchment paper.

Chill the cookie dough balls in the fridge for about 20 minutes. Preheat your oven to 350°F (about 175°C) and line baking sheets with parchment paper.

After chilling, transfer 12 cookie dough balls to the lined cookie sheet, spacing them about 2 inches apart. Bake in the preheated oven until nearly baked through, about 12 to 14 minutes.

Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.

Serve peppermint cookies on their own or with hot chocolate, coffee, or tea. They also work well on dessert platters or as ice cream sandwich cookies.