Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, cornstarch, baking soda, baking powder, and salt in a bowl.
Cream butter, granulated sugar, and brown sugar until light and fluffy, 2–3 minutes.
Beat in eggs one at a time, then mix in vanilla and peppermint extract.
Mix in dry ingredients on low just until combined; do not overwork the dough.
Fold in peppermint chips, white chocolate chips, and most of the crushed candy.
Scoop 1.5-tablespoon mounds onto sheets, spacing 2 inches apart. Sprinkle with reserved candy.
Bake 10–12 minutes, until edges are set and centers look slightly soft.
Cool 5 minutes on the sheet, then transfer to a rack to finish cooling.