1. Preheat oven to 375 degrees F. Line two baking pans with parchment paper and set aside.
2. Using a stand mixer or electric beaters, cream butter, brown sugar, and granulated sugar together on medium speed, beat until creamy, for about 2 minutes. Add in egg and vanilla and mix just until incorporated on low speed.
3. Scrape down the sides of the bowl if needed. Add the baking soda, salt, and cornstarch. Mix just until combined then gradually beat in the flour.
4. Add the chocolate chips and Andes Mints and either beat for a few seconds on low speed or fold in by hand.
5. If time permits, I suggest chilling the dough for at least 30 minutes or up to 1 day. This will make it thicker and more flavorful. After chilling, if needed, let the dough sit at room temperature to soften it enough to make it easier to scoop out cookie dough balls.
6. Scoop about 2 tablespoons of dough into balls and place them evenly spaced on the prepared cookie sheets.
7. Bake for 8-10 minutes until edges are just golden. Make sure not to over bake, the cookies will set up as they cool. Remove from oven and immediately if desired, add more Andes Mints to the top of the cookies.
8. Let cool on baking sheet for 5-10 minutes, and then transfer to wire rack to finish
cooling. (Store in an airtight container for up to 5 days.)