Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, cocoa, baking soda, cornstarch, espresso powder, and salt in a bowl.
Cream butter, granulated sugar, and brown sugar until light and fluffy.
Beat in eggs, vanilla, and peppermint extract until smooth.
Mix in dry ingredients on low just until combined. Do not overmix.
Fold in chocolate chips and half of the crushed peppermint.
Scoop 1½-tablespoon mounds, spacing about 2 inches apart on sheets.
Bake 9–11 minutes, until edges are set and tops look slightly soft.
Sprinkle remaining peppermint over hot cookies. Cool 5 minutes on sheets.
Transfer to a rack and cool completely for crisp edges and chewy centers.