Preheat your oven to 350°F. In a bowl, mix the shredded chicken with 1 cup of cheese. Fill each tortilla with this mixture, roll them up, and place seam-side down in a lightly greased 9×13-inch baking dish.

In a small skillet over medium heat, melt the butter. Stir in the flour and cook for about 1 minute, creating a blonde roux. Gradually add the chicken broth while whisking until the sauce becomes smooth and starts to thicken.

Remove the sauce from heat. Stir in the sour cream and diced green chiles until fully incorporated.

Pour the creamy sauce evenly over the enchiladas. Top with the remaining 1 cup of cheese. Bake in the preheated oven for 20–25 minutes, or until the cheese is melted and bubbly.

Remove from the oven, let the dish rest for a minute, and enjoy while hot. These enchiladas pair well with a simple side salad, Spanish rice, or refried beans.