Preheat oven to 350 °F (175 °C). Lightly grease a 9×13-inch baking dish.

In a large bowl, combine shredded chicken, 1 cup Monterey Jack cheese, ½ cup cheddar cheese, garlic powder, ground cumin, salt and pepper. Mix well.

Warm the flour tortillas (microwave wrapped in towel ~30 seconds or heat in dry skillet) to make them pliable.

Spoon about ½ cup of the chicken mixture into each tortilla, roll and place seam-side down in the prepared baking dish.

In a medium saucepan over medium heat, melt butter. Whisk in flour and cook 1-2 minutes.

Gradually whisk in chicken broth until smooth and thickened, then remove from heat and let cool ~1 minute.

Whisk in sour cream and diced green chiles until smooth. Season with salt and black pepper.

Pour the white sauce evenly over the assembled enchiladas, spreading to the edges. Sprinkle remaining 1 cup Monterey Jack and remaining ½ cup cheddar cheese on top.

Bake uncovered for 25-30 minutes until cheese is melted and sauce is bubbly. Optional: broil 2-3 minutes for golden top.

Remove from oven, let rest 5 minutes, garnish with chopped cilantro, green onions or diced tomato/avocado, then serve.