Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the softened butter, brown sugar, and granulated sugar. Beat until light and fluffy, about 2-3 minutes.
Add the egg, vanilla extract, and peppermint extract to the creamed mixture. Beat until well combined.
In a separate bowl, whisk together the all-purpose flour, cocoa powder, cornstarch, baking soda, and salt.
Gradually add the dry mixture to the wet ingredients, mixing on low speed until just combined.
Gently fold in the mint M&Ms with a spatula until evenly distributed.
Drop rounded balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart. Bake for 10-12 minutes.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack.