Step 1: In a large bowl, combine the shredded chicken, drained green chiles, half of the shredded Pepper Jack cheese, and half of the softened cream cheese. Mix well to ensure all ingredients are evenly distributed.
Step 2: Prepare the sauce. In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux. Gradually whisk in the chicken broth and heavy cream until smooth. Bring to a simmer, stirring until the sauce thickens.
Step 3: Remove the sauce from heat and stir in the remaining half of the softened cream cheese until it is fully melted and the sauce is smooth and creamy. Season the sauce with garlic powder, salt, and black pepper to taste.
Step 4: Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish. Pour about 1/2 cup of the prepared sauce into the bottom of the dish and spread evenly.
Step 5: Warm the tortillas briefly (microwave for 15-20 seconds or dip in warm sauce) to make them pliable. Take one tortilla, spoon about 1/4 to 1/3 cup of the chicken mixture down the center, and roll it up tightly. Place seam-side down in the prepared baking dish.
Step 6: Repeat with the remaining tortillas and filling, arranging them snugly in the baking dish.
Step 7: Pour the remaining green chile cream sauce evenly over the rolled enchiladas. Sprinkle the remaining shredded Pepper Jack cheese over the top.
Step 8: Bake for 20-25 minutes, or until the sauce is bubbly and the cheese is melted and lightly golden. If desired, broil for 1-2 minutes for a crispier top. Let stand for 5-10 minutes before serving.
Step 9: Serve hot, garnished with fresh cilantro, avocado, or sour cream if desired. Enjoy your delicious Green Chile and Pepper Jack Cheese Chicken Enchiladas!