Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, cornstarch, baking powder, baking soda, and salt in a bowl.
Beat softened butter and cream cheese until completely smooth and creamy.
Add granulated and brown sugars. Beat until pale and fluffy, about 2 minutes.
Mix in vanilla until combined.
Add dry ingredients and mix on low just until no dry spots remain. If crumbly, splash in the milk.
Fold in white chocolate chips, crushed raspberries, and lemon zest.
Scoop 1½-tablespoon mounds onto sheets, spacing about 2 inches apart. Chill the trays 15 minutes.
Bake 11–12 minutes, until edges set and tops look matte but pale.
Cool on the sheet 5 minutes, then transfer to a rack to finish cooling.