Preheat oven to 350 degrees. Use parchment paper or a silpat mat to line a baking sheet.
Cream the butter, brown sugar and sugar in a stand mixer until light and fluffy (about 2-3 minutes). Scrape the sides of the bowl to make sure all ingredients are blended.
Add in the egg, vanilla and peppermint extract and beat until combined.
Add in flour, baking soda, cornstarch and salt. Stir until all combined.
Stir in chocolate chips.
Scoop out about 1 TBSP of dough for smaller cookies (or 1/4 cup dough for BIG cookies). Place dough balls on prepared pan (12 cookies to a pan if small cookies and 6 to a pan if BIG cookies).
Bake for about 10-11 minutes. Remove from oven. Let cool on tray for 5 minutes. Transfer cookies to cooling rack. NOTE: Baking time will be longer if you make BIG cookies.
Melt the white chocolate chips and vegetable shortening in the microwave for 45 seconds. Stir and continue melting 15 seconds at a time until fully melted.
Spoon about 1 tsp of melted white chocolate on top of each cookie. Carefully spread chocolate and sprinkle with crushed candy canes.