Heat oven to 350°F. Line two baking sheets with parchment.
Beat butter and cream cheese until completely smooth and creamy.
Add granulated and brown sugars. Cream until light and fluffy.
Mix in vanilla and peppermint extracts until combined.
Whisk flour, cornstarch, baking powder, baking soda, and salt in a bowl.
Add dry ingredients to the mixer in two additions. Mix just until a soft dough forms.
Fold in white chocolate chips and crushed peppermint candies.
Scoop 1½-tablespoon mounds onto sheets, spacing 2 inches apart.
Bake 10–12 minutes, until edges are set and tops look slightly matte.
Press a pinch of extra peppermint on warm cookies, if using. Cool 5 minutes, then move to a rack.