Preheat your oven to 375°F (190°C).

In a mixing bowl, combine your shredded cooked chicken with a small handful of shredded Monterey Jack cheese and a spoonful of green chiles. Stir the mixture gently until just combined.

In a medium saucepan, melt 3 tablespoons of butter over medium heat, then whisk in ¼ cup of flour to create a roux. Cook for about 1-2 minutes until it turns light golden.

Gradually whisk in 2 cups of chicken broth, stirring continuously until the mixture thickens, about 3-5 minutes. Fold in 1 cup of sour cream and the remaining green chiles.

Take your flour tortillas, place about 3 tablespoons of the chicken mixture in each, roll tightly, and place them seam-side down in a greased baking dish.

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

Bake in the preheated oven for 20-25 minutes until the cheese is melted and bubbly.

Let the enchiladas sit for a few minutes to set, then garnish with diced tomatoes and fresh cilantro before serving.