Line two baking sheets with parchment paper and preheat the oven to 400 F.
Make the egg wash: beat one whole egg with a tbsp of water in a small bowl. Set aside.
Make the cream cheese filling: mix the softened cream cheese, egg yolk, sugar, lemon juice, and ½ tsp vanilla extract in a medium-sized bowl using a whisk, until smooth.
Place one sheet of thawed puff pastry on each baking sheet and cut into 4 squares.
Fold the corners of the squares over by one inch to make octagons.
Spoon about 2 tbsp of cream cheese filling into the middle of each square (do not spread it). Brush them with egg wash and dust them with sugar.
Bake for 18-20 minutes or until puffed and golden brown. Let them cool down a bit.
Make the icing: mix the confectioner’s sugar, milk, and ½ tsp vanilla extract until smooth. Drizzle on top of the slightly cooled danishes.