Preheat the oven to 400°F and line a baking sheet with parchment paper.
Use a stand mixer with a paddle attachment and cream together butter and sugars on low speed until light and fluff. Approximately 4 minutes.
Add the egg, vanilla extract, salt, baking soda, and cornstarch. Mix until smooth; making sure to scrape down the sides of the bowl as necessary.
Turn the mixer to low and gradually add the flour in with the wet ingredients, mixing until combined.
On a cutting board, finely chop the peppermint chocolate pieces. Put the oreos into a plastic bag and use your hands to crush them. Then, use a rubber spatula to fold in the oreo pieces and peppermint crunch pieces. Save a few pieces for the top of each cookie.
Using a 1.5 tbsp cookie scoop (medium sized), scoop balls of cookie dough onto the parchment-lined baking sheet then press your extra cookies and peppermint bits into the tops of the cookies. Recipe makes ~12 large cookies.
Bake the cookies for 8-10 minutes or until the edges are golden brown and middles have begun to set. Note: middles may look slightly underdone. They will continue to bake as they cool on the pan.
After 10 minutes, transfer from the hot baking sheet to a cooling rack to finish cooling. Enjoy!