Preheat the oven to 350°F (180°C, 160°C fan) and line a large baking sheet with parchment paper.
For the cheesecake filling, mix cream cheese, egg yolk, powdered sugar, lemon juice, vanilla, and salt in a bowl using a whisk or rubber spatula.
Roll out the puff pastry into a 12×12-inch square using a rolling pin.
Cut the dough into nine 4-inch squares using a pizza cutter or knife. Fold each corner of the squares about 1 inch toward the center, pressing gently to seal.
Place a tablespoon of the cream cheese filling in the center of each puff pastry square using a small cookie scoop.
Prepare the egg wash by whisking together the egg and water in a small bowl. Brush the edges of each pastry surrounding the filling.
Bake for 16-18 minutes, rotating the baking sheet halfway through. Allow the pastries to cool completely on a wire rack.
For the glaze, gradually mix powdered sugar, milk, and vanilla extract in a bowl to avoid a runny consistency. Drizzle the glaze over each cooled pastry.
