In a medium saucepan over medium heat, melt 4 tablespoons of unsalted butter until frothy but not browned.

Whisk in 1/4 cup of all-purpose flour and cook for about 1 minute until lightly golden.

Gradually whisk in 2 cups of low-sodium chicken broth, continue whisking until sauce thickens.

Stir in 4 ounces of diced green chilies and 1 cup of sour cream until smooth.

In a large bowl, combine 2 cups of cooked shredded chicken, 6 ounces of cream cheese, and 1 cup of shredded Monterey Jack cheese; mix well.

Preheat your oven to 350°F (175°C) for even baking.

Spread a thin layer of creamy sauce on the bottom of a baking dish.

Lay out tortillas and fill each with about 1/4 cup of chicken mixture; roll and place seam-side down in the dish.

Pour remaining sauce over the enchiladas and sprinkle with 1 cup of shredded cheese.

Cover with foil and bake for 20 minutes, then remove foil and bake an additional 5 minutes until golden.