1. Mix the dry ingredients:In a medium mixing bowl, whisk together the flour, corn starch, baking soda, and salt.

2. Beat the wet ingredients: In the bowl of a stand mixer fitted with the paddle attachment (or using a large bowl and handheld electric mixer), beat together the butter, cream cheese, brown sugar, and granulated sugar until light and creamy. Add the egg and yolk one at a time, beating each in until fully incorporated and scraping down the bowl/beater as needed. Beat in the vanilla and peppermint extracts.

3. Add the dry ingredients to the wet and mix in on lowest speed until mostly incorporated. Add the peppermint candy and white chocolate chips and fold in by hand just until evenly dispersed into the cookie dough.

4. Chill and portion dough: Chill cookie dough in refrigerator for at least one hour before baking. When ready to bake, preheat oven to 350ºF with racks in the top and bottom-third positions. Scoop dough into 2 1/4 ounce (or about 1/4 cup) portions and roll each into a ball. If desired, roll the tops and sides of each cookie dough ball in extra crushed candy cane pieces. Place on baking sheets lined with parchment paper or silicone liners, spreading well apart with no more than 6 balls of dough per sheet. 

5. Bake cookies at 350ºF for 14-16 minutes, until tops no longer look wet and cookies are puffy, flipping and rotating baking sheets halfway through time. Top each cookie with a few extra white chocolate chips, and cool on pan for 10-15 minutes before carefully transferring to a wire rack to cool completely. Store in an airtight container for up to a few days, or in the refrigerator for longer storage.