In a medium-sized mixing bowl, whisk together the flour, corn starch, baking soda, and salt. Set aside.
Melt the butter and let it cool for 5 minutes. In a large bowl, whisk together the melted butter, brown sugar, and sugar until combined. Add the egg, vanilla extract, and peppermint extract and whisk until incorporated.
Add the flour mixture to the bowl and mix together with a wooden spoon or silicone spatula just until combined. Then fold in the mini chocolate chips and Junior Mints. Cover the bowl with saran wrap and place into the refrigerator to chill for 2 HOURS (chilling the cookie dough prior to baking is mandatory).
Preheat the oven to 350 degrees and line your baking sheets with silicone baking mats. Use a 1.5 tablespoon cookie scoop to scoop out the dough into your hands. Shape the cookie dough into a ball and place onto the prepared baking sheet. Press into the dough extra chocolate chips and half of a Junior Mint (optional).
Bake for 9-11 minutes (10 minutes is perfect for me), and allow the cookies to cool on the pan for 10 minutes before transferring them over to a wire cooling rack. If the cookies spread too much or some of the Junior Mints ooze out from the cookies, use a circular cookie cutter to "rotate" the cookies back into place (see notes below). The cookies will look slightly underdone when you remove them from the oven but they're not. Just let them cool for those 10 minutes before removing them.
Keep any leftover cookies in an airtight container on the counter for up to 7 days.