Preheat oven to 375°F. In a large bowl, toss together chicken, tomato sauce, minced chipotle peppers, and 3 tablespoons cilantro; then stir in the cheese.
Spoon 2 heaping tablespoons of the cooked chicken mixture onto the middle of a puff pastry round. Moisten the edges of the pastry with the beaten egg and fold it in half to form a half-moon shape. With a fork, press the edge of the empanada to seal, then transfer to a greased baking sheet.
Repeat with remaining puff pastry rounds and filling to make 12 empanadas. Brush empanada tops with beaten egg.
Bake until empanadas are puffed and golden brown and filling is hot, about 20 minutes, rotating the pan after 10 minutes for even browning.
Transfer empanadas to a cooling rack. If desired, sprinkle with 1 tablespoon cilantro; serve warm or room temperature, with the Cilantro Crema.