Add chicken breasts to a small casserole pan along with 1/4 cup water. Cover and cook until chicken is no longer pink and reaches 175 degrees, approximately 45-50 minutes. Allow to cool enough to handle. Note: chicken can also be cooked in water on the stovetop.
Discard skin and bones, shred chicken with a fork and add to a mixing bowl. Add remaining filling ingredients, except tortillas, and toss to combine.
Add butter or Ghee to a large skillet, turn to medium, and melt. Add flour and cook for 1 minute. Slowly stir in broth and stir continuously until it slightly thickens, about 3-5 minutes. Reduce heat slightly, add sour cream, 1 can diced green chills, black pepper, salt, chili powder, and 1 cup cheese, stir just until cheese is melted.
Add 1/2 cup sauce in a 9 x 13-inch casserole pan and spread across the bottom. Layer 1/3 tortilla halves on the bottom. Spread half the chicken mixture over the tortillas, top with 1/3 tortillas, add the remaining chicken filling and top with remaining tortillas. Pour remaining sauce over the top. Sprinkle with the 1/2 cup cheese.
Loosely cover the casserole with foil and bake until bubbly, about 25 minutes. Remove foil and bake an additional 5 minutes, or until cheese is lightly golden. Sprinkle with chopped cilantro before serving.