Preheat oven to 400F. Line two baking sheets with parchment paper.
Beat the whole egg with about 1 tbsp of water in a small bowl. Then Set aside. With the second egg, separate egg white from egg yolk.
In a medium bowl mix together egg yolk, cream cheese, sugar, lemon juice, lemon zest, and vanilla. Mix until smooth.
Lay out the sheets of the puff pastry and cut each into 4 squares.
Fold the corners of the squares over by about 1 inch to make an octagon shape.
Brush the pastry puff with the egg wash.
Spoon the cream cheese mixture into the center of each puff pastry. (About 2 tablespoons). Sprinkle coarse sugar over pastry.
Bake in the oven for about 18-20 minutes and golden brown all over.