Preheat oven to 350°F. Grease a 9x13-inch baking dish and set aside.

In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute. Gradually whisk in chicken broth and cook until thickened, about 3-4 minutes. Remove from heat and stir in sour cream, green chiles, salt, and pepper.

In a large bowl, combine shredded chicken with 1 cup of the cream sauce and 1 cup of shredded cheese. Mix well.

Spoon about 1/3 cup of chicken mixture down the center of each tortilla. Roll up tightly and place seam-side down in the prepared baking dish.

Pour the remaining cream sauce evenly over the enchiladas. Sprinkle the remaining 2 cups of cheese on top.

Bake uncovered for 25-30 minutes, until the cheese is melted and bubbly and the edges are lightly golden.

Let stand for 5 minutes before serving. Garnish with fresh cilantro, sliced jalapeños, or additional sour cream if desired.