In a stand mixer bowl, blend melted butter, granulated sugar, light brown sugar, vanilla extract, and peppermint extract. Mix on medium for 1 minute.
Add eggs and mix on low until incorporated. Add flour, corn starch, cocoa powder, baking soda, and salt. Mix on low until everything is combined.
Line a baking sheet with parchment paper. Use a medium cookie dough scoop (about 2.5 tablespoons per ball) to make 20 even cookies. Refrigerate for 30 minutes to enhance flavor and prevent spreading.
Preheat the oven to 350°F. Space the chilled cookie dough 2 inches apart on the baking sheet and bake for 9-10 minutes, until the edges are just set. Let cool on the sheet for 3 minutes before transferring to a rack to cool completely.