In a medium saucepan over medium heat, melt the butter until bubbling gently. Whisk in the flour, cooking for about 2 minutes until golden. Gradually add the chicken broth, continuously whisking until the mixture thickens and coats the back of a spoon, approximately 5 minutes. Remove from heat and stir in the sour cream, cumin, and salt and pepper to taste.

In a large mixing bowl, combine the shredded chicken, finely diced onion, diced green chiles, and cilantro. Mix in 1 cup of the cheese mixture, ensuring everything is well distributed.

Preheat your oven to 350°F (175°C). Spread about 1/2 cup of the white sauce on the bottom of a greased baking dish. Take a tortilla, fill it with a portion of the chicken mixture, and roll tightly. Place each seam-side down in the baking dish.

Pour the remaining white sauce over the enchiladas, then sprinkle the remaining cheese on top. Bake for 25-30 minutes or until bubbling and golden brown. Let sit for 5 minutes before slicing.