Preheat your oven to 400°F (200°C).
In a mixing bowl, combine the softened cream cheese, queso fresco, chili powder, ground cumin, crushed red pepper flakes, Pepper Jack cheese, scallions, and shredded or cubed cooked chicken. Stir until everything is well mixed.
If using homemade pie crust, roll out your dough on a lightly floured surface until it's about 1/8 inch thick. If using store-bought, simply unroll the pie crusts.
Using a round cutter or a small bowl, cut out circles from the dough, each about 4-5 inches in diameter.
Place about 2 tablespoons of the chicken filling in the center of each dough circle. Be careful not to overfill.
Fold the dough over the filling to create a half-moon shape. Press the edges together to seal, then use a fork to crimp the edges.
In a small bowl, whisk together the egg and water to create an egg wash. Brush the tops of each empanada with the egg wash.
Place the empanadas on a parchment-lined cookie sheet. Bake in the preheated oven for 20-25 minutes, or until golden brown.
Once baked, remove the empanadas from the oven and let them cool slightly before serving.