Preheat the oven to 350°F(175°C). Line a large baking sheet with parchment paper.
In a mixing bowl, whisk together the cream cheese, egg yolk, powdered sugar, lemon juice, vanilla, and salt.
Roll out the puff pastry into a 12”×12” square. Cut the dough into 9 squares. Fold the corners of each square in toward the center (about 1”) and press lightly to hold it there.
Scoop 1 tablespoon of the cream cheese filling into the center of the puff pastry squares.
In a small bowl, whisk together the egg and water. Use a pastry brush to brush the sides of each pastry, around the filling.
Bake for 16-18 minutes. If the pastries are not cooking evenly, rotate the baking sheet halfway through.
In a bowl, combine the powdered sugar and vanilla extract. Slowly add the milk, just until the icing is pourable. You might not need all of the milk.
Remove the pastry from the oven and cool completely. Drizzle icing over the pastries before serving.