Preheat oven to 400°F. Line two baking sheets with parchment.
Beat cream cheese, sugar, lemon zest, lemon juice, and vanilla until smooth and fluffy.
Unfold puff pastry and gently roll seams flat on a lightly floured surface.
Cut pastry into 8 even squares and arrange on the sheets.
Score a 1/2-inch border on each square and dock centers with a fork.
Brush pastry tops and borders lightly with milk.
Spoon a heaping tablespoon of filling into each center, staying inside the border.
Bake 16–19 minutes until puffed and deep golden. Cool 5 minutes.
Whisk powdered sugar with lemon juice; add a splash of milk to reach drizzle consistency.
Drizzle glaze over warm pastries and serve.