Preheat oven to 350°F. Line two baking sheets with parchment paper.
Beat filling cream cheese, powdered sugar, vanilla, and lemon zest until smooth. Chill 10 minutes.
Whisk flour, cornstarch, baking powder, baking soda, and salt in a bowl.
Cream softened butter, dough cream cheese, granulated sugar, and brown sugar until light and fluffy.
Mix in vanilla and milk until combined.
Add dry ingredients to the creamed mixture. Mix just until a soft dough forms.
Fold in crushed freeze-dried strawberries and white chocolate chips. Chill briefly if sticky.
Scoop 1½-tablespoon mounds onto sheets, spacing about 2 inches apart.
Press a shallow well in each mound. Spoon a small dollop of cheesecake filling into the center.
Top each with a tiny dab of strawberry jam and gently swirl with a toothpick.
Bake 11–13 minutes, until edges are set and tops look matte. Do not overbake.
Cool 10 minutes on the sheet, then transfer to a rack to finish cooling.