Preheat the oven to 350°F/180°C, 160°C fan oven, and line a large cookie sheet with parchment paper (I used a half-size sheet pan).
To make the cheesecake filling, in a bowl combine cream cheese with yolk, powdered sugar, lemon juice, vanilla, and salt. Use a whisk or a rubber spatula.
Using a rolling pin, roll out the puff pastry into a 12x12-inch square.
Use a pizza cutter or a knife, cut the dough into 9 4-inch squares. Then fold each corner of each square about 1 inch towards and center and press gently to adhere.
With the help of a small (1 tablespoon) cookie scoop, scoop a tablespoon of cream cheese filling into the center of each puff pastry square.
Make the egg wash, in a small bowl whisk together an egg with water, then using a pastry brush, brush the sides of each pastry (everywhere around the filling).
Bake in the preheated oven for 16-18 minutes rotating the pan halfway through. Remove from the oven, and allow to cool completely before adding the icing.
To make the icing, in a bowl, combine the powdered sugar with milk and vanilla extract. Very slowly add the milk so you don’t end up with a thin icing. Drizzle over each pastry.