1. Preheat your oven to 350°F (175°C) and grease a 9×13-inch baking dish.
2. In a large bowl, combine the sour cream, salsa, cream of chicken soup, diced green chilies, chili powder, cumin, salt, and pepper. Mix well until all the ingredients are incorporated.
3. Add the shredded chicken to the sour cream mixture and stir until the chicken is evenly coated.
4. Take a tortilla and spoon a generous amount of the chicken mixture onto the center of the tortilla. Roll it up and place it seam side down in the prepared baking dish. Repeat with the remaining tortillas and chicken mixture until the dish is filled.
5. Pour any remaining sauce over the rolled tortillas, making sure they are well coated. Sprinkle the shredded cheese evenly over the top.
6. Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes. Then remove the foil and continue baking for an additional 10-15 minutes, or until the cheese is melted and bubbly.