Preheat oven to 375°F (190°C).
In a bowl, combine the shredded chicken with ½ 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 1-2 minutes.
Slowly whisk in chicken broth and bring to a simmer until thickened.
Remove from heat and stir in sour cream and remaining green chiles. Mix until smooth.
Spoon chicken mixture into each tortilla, roll up, and place seam-side down in a greased baking dish.
Pour the sour cream sauce over the enchiladas, spreading evenly.
Top with the remaining shredded cheese.
Bake uncovered for 20-25 minutes, until bubbly and golden.
Garnish with diced tomatoes and cilantro if using. Let rest 5 minutes before serving.
