Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.

In a medium saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute to create a roux.

Gradually whisk in chicken broth until smooth. Continue cooking until the sauce thickens and begins to bubble.

Remove saucepan from heat and stir in sour cream, diced green chiles, salt, and pepper until well combined.

Spread a small amount of the sauce on the bottom of the prepared baking dish.

Layer half of the tortilla strips, half of the shredded chicken, and one-third of the cheese in the dish.

Pour half of the remaining sauce over the layers.

Repeat layers with the remaining tortillas, chicken, and half of the remaining sauce.

Top with the remaining cheese.

Bake for 25 to 30 minutes until the sauce is bubbly and the cheese is melted and lightly browned.

Let stand for 5 minutes before garnishing with cilantro and serving.