In a large bowl, using a hand mixer, cream the butter and sugar until light and fluffy.
Add the egg, vanilla, and peppermint oil into the large bowl. Mix just until fully incorporated - for 15-20 seconds. Don't mix any longer, your cookies will be stiff.
Sift or whisk together the flour, baking soda, baking powder, and salt into a medium bowl and mix until fully incorporated.
Slowly add the dry ingredients to the wet ingredients, mixing again until fully incorporated and scraping the sides of the bowl as needed.
Fold in ¾ of the white chocolate chips and ¾ of the crushed candy canes.
Chill the dough for 30 minutes in the refrigerator.
Preheat the oven to 350℉ (176.667℃). Lie a baking sheet with parchment paper and set aside.
Use a cookie scoop or measuring spoon to scoop 2 Tablespoons of dough. Use clean hands to roll the dough into a ball and place them on the prepared baking sheet.
Bake for 5 minutes.
Remove the cookies from the oven and place the remainder of the white chocolate chips and crushed candy canes on top of each cookie.
Bake for an additional 2 minutes.
Remove from the oven and allow them to cool for 2 minutes on the baking sheet and then place the cookies onto a wire rack.