Preheat oven to 375°F (190°C). Grease a 9x13 inch baking dish.

In a large mixing bowl, combine the shredded chicken with 1/2 cup of the shredded cheese and half of the diced green chiles.

Melt butter in a saucepan over medium heat. Whisk in the flour and cook for 1 to 2 minutes until it forms a golden roux.

Slowly whisk in chicken broth and bring to a simmer, stirring until thickened, about 3 to 4 minutes.

Remove from heat and stir in sour cream and remaining green chiles. Mix until smooth.

Warm tortillas briefly to make them pliable. Spoon about 3 tablespoons of chicken mixture into each tortilla, roll up, and place seam-side down in the greased baking dish.

Pour the sour cream sauce over the enchiladas, spreading evenly.

Top with the remaining 1.5 cups of shredded cheese.

Bake uncovered for 20 to 25 minutes, until bubbly and golden.

Let rest 5 minutes before serving. Garnish with diced tomatoes and cilantro if using.