Melt butter in a large saucepan over medium heat. Whisk in flour and cook for 1 minute, stirring constantly, until you have a smooth paste and it turns light golden.

Gradually add chicken broth to the roux, whisking constantly to prevent lumps. Keep whisking until the sauce thickens and becomes smooth, about 3-4 minutes.

Remove from heat and stir in sour cream, cumin, salt, and pepper until perfectly combined.

In a mixing bowl, combine shredded chicken, diced onion, green chiles, cilantro, and 1 cup of the cheese mixture. Mix thoroughly for a well-distributed filling that delivers flavor in every bite.

Preheat the oven to 350°F. Spread a thin layer of white sauce in the bottom of a greased 9x13 baking dish.

Place about 1/3 cup of the chicken mixture down the center of each tortilla, roll tightly, and arrange seam-side down in the prepared dish.

Pour remaining white sauce evenly over rolled enchiladas, ensuring they’re completely covered. Sprinkle remaining Monterey Jack and cheddar cheese over the top.

Bake uncovered at 350°F for 25-30 minutes until the sauce bubbles around the edges and the cheese is melted and golden brown.

Remove from the oven and let rest for 5 minutes before serving to allow the sauce to set properly.