In a medium bowl, mix together the flour, cornstarch, baking soda, salt, peppermint baking chips and white chocolate chips.
In the bowl of a mixer, cream together the butter, brown sugar, and granulated sugar until light and fluffy.
Mix in the egg and vanilla extract, scraping down the sides of the bowl as needed, until fully combined.
Slowly add the dry ingredients to the wet ingredients, mixing just until combined.
Line a baking sheet with parchment paper. Scoop the cookie dough using a 1-ounce scoop, or two heaping tablespoons and place dough balls 2 inches apart. Gently press down to slightly flatten.
Refrigerate the dough for at least 2 hours or up to overnight.
Preheat the oven to 350°F. Bake the cookies for 14 minutes, until the edges are set and the centers look slightly underbaked.
Cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely. Enjoy!