Add chopped apricots to a saucepan and cover with water. Bring to a boil and then turn down to simmer, cooking until the apricots have softened, about 20 minutes. Add additional water if needed. There should be some extra fluid when you are finished. If not, add a little more water. Add ½ cup of sugar to the softened apricots and cook over medium heat until the sugar has dissolved, about 2-3 minutes.
Drain the apricots reserving the liquid, you will need about 2 tablespoons of the liquid. Allow to cool.
Preheat oven to 350º. Line a baking sheet with parchment paper.
In a medium bowl, combine the cream cheese, ricotta, powdered sugar, lemon zest, and vanilla and mix with a hand held mixer until smooth.
If using Dufour puff pastry, cut it in half and roll each half into a 10 inch square on a lightly floured surface. If using Pepperidge Farm puff pastry, roll each sheet into a 10 inch square. Cut into 8 squares total.
Add about 2 tablespoons of the cream cheese filling into the center of each puff pastry square. Add about a teaspoon of the apricot filling on top of the cream cheese filling.
Mix the egg with a tablespoon of water and brush onto two opposite corners of each square. Take one corner and place it across the filling and do the same with the opposite corner.
Brush the outside of the puff pastry with the reserved apricot liquid.
Bake for 20-23 minutes until the puff pastry is golden brown. Let cool slightly. Can eat warm or at room temperature.