In a mixing bowl, combine shredded cooked chicken, a handful of shredded Monterey Jack cheese, and diced green chiles until everything is evenly mixed.

In a medium saucepan over medium heat, melt butter until bubbly. Whisk in all-purpose flour to create a roux, cooking for about 1 minute until golden.

Gradually add chicken broth while whisking to prevent lumps. Simmer until the sauce thickens, roughly 5-7 minutes, then stir in sour cream along with chopped green chiles.

Take a flour tortilla and spread a few tablespoons of the chicken mixture along the center. Roll up the tortilla tightly and place it seam-side down in a greased baking dish.

Pour the creamy sour cream white sauce generously over the rolled enchiladas and sprinkle the remaining shredded cheese on top.

Preheat your oven to 375°F (190°C) and bake uncovered for 20-25 minutes until the edges are bubbly and the cheese is golden and slightly crispy.

Let the enchiladas cool for about 5 minutes and garnish with diced tomatoes and fresh cilantro before serving.