Melt butter in a large saucepan over medium heat.

Whisk in flour and cook for 1 minute, stirring constantly, until it forms a smooth paste and turns light golden.

Gradually add chicken broth to the roux, whisking constantly to prevent lumps. Continue 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 to create a well-distributed filling.

Preheat 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 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 the remaining Monterey Jack and cheddar cheese over the top.

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

Remove from the oven and let rest for 5 minutes before serving.