Preheat the oven to 400 degrees Fahrenheit (200 degrees Celsius) and line two baking sheets with parchment paper.
In a large mixing bowl, combine the shredded chicken, cream cheese, cheddar cheese, parsley, garlic powder, onion powder, salt, and pepper until the mixture is uniform.
On a lightly floured surface, unfold the puff pastry sheets and cut each sheet into four equal squares, resulting in eight squares total.
Distribute the chicken mixture evenly by placing approximately 1/4 cup onto the center of each pastry square.
Fold one corner of the pastry over the filling to the opposite corner to form a triangle; crimp the edges firmly with a fork to seal.
In a small bowl, whisk the egg and water together to create an egg wash.
Place the pastries on the prepared baking sheets, brush the tops with egg wash, and cut a small vent in the center of each pastry.
Bake for 18 to 22 minutes or until the pastry is puffed and golden brown.
Remove from the oven and let rest for 5 minutes before serving.