Preheat the oven to 350°F (175°C) and lightly grease a 9×13-inch baking dish.
In a mixing bowl, combine the shredded chicken, 1 cup of shredded cheese, and salt and pepper to taste.
Fill each tortilla with a portion of the chicken mixture, fold them closed, and arrange them seam-side down in the prepared baking dish.
In a medium saucepan over medium heat, melt the butter. Stir in the flour and cook until smooth and lightly bubbling.
Gradually whisk in the sour cream and chicken broth until the sauce is creamy and smooth.
Stir in the diced green chiles and additional salt and pepper as desired. Continue cooking until the sauce thickens slightly.
Pour the creamy sauce evenly over the filled tortillas. Sprinkle the remaining 1 cup of shredded cheese on top.
Bake in the preheated oven for 20–25 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let cool slightly before serving. Enjoy!
Enjoy!