Make the White Sauce: Melt 4 tablespoons of butter in a medium saucepan over medium heat. Whisk in 1/4 cup of all-purpose flour, stirring constantly for about 2 minutes until light golden brown. Gradually add 2 cups of chicken broth, whisking until thickened, about 5-7 minutes. Stir in 1 cup of sour cream, 1 teaspoon of cumin, salt, and pepper, until smooth.

Prepare the Filling: In a mixing bowl, combine 2 cups of shredded chicken, 1/2 cup of diced onion, 1 can of diced green chiles, and 1/4 cup of chopped fresh cilantro. Mix in 1/2 cup each of shredded Monterey Jack and Cheddar cheese.

Assemble the Enchiladas: Preheat oven to 350°F (175°C). Spread 1/2 cup of the creamy white sauce in a 9x13 dish. Fill each tortilla with 1/3 cup of filling and roll tightly, placing seam-side down in the dish.

Add the Sauce and Cheese: Pour remaining creamy white sauce over assembled enchiladas. Sprinkle remaining shredded cheese on top.

Bake: Bake in preheated oven for 25-30 minutes until bubbling and cheese is golden. Edges should be light brown.

Resting Time: Allow to sit for 5 minutes before serving to let the sauce set.