Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper.
In a mixing bowl, combine the shredded chicken, softened cream cheese, green onions, garlic powder, thyme, salt, and pepper until well incorporated.
Unroll the puff pastry sheets on a lightly floured surface and cut each sheet into four 5-inch squares.
Place approximately 3 tablespoons of the chicken filling into the center of each pastry square.
Fold the pastry over the filling to form a triangle and use a fork to crimp and seal the edges tightly.
Whisk the egg and water in a small bowl to create an egg wash.
Brush the tops of each pastry turnover with the egg wash and cut a small slit in the top for steam to escape.
Bake for 20 to 25 minutes or until the pastry is puffed and deep golden brown.
Remove from oven and let rest for 5 minutes before serving.