In a large mixing bowl, combine the softened cream cheese, sour cream, half of the Monterey Jack cheese, half of the cheddar cheese, and the diced green chiles. Add the garlic powder, cumin, chili powder, and a pinch of salt and pepper. Stir until everything is well combined.

Fold the shredded chicken into the cheese mixture until it is evenly coated.

Preheat your oven to 375 degrees F. Lightly grease a 9x13 inch baking dish.

Lay a tortilla on a clean work surface. Spoon about 1/4 cup of the chicken filling down the center of the tortilla. Roll it up tightly and place it seam side down in the prepared baking dish. Repeat with the remaining tortillas.

In a small saucepan, warm the chicken broth over medium heat. Whisk in the remaining cream cheese and sour cream if you reserved any, or simply use a little extra broth. The goal is a smooth, pourable sauce. Simmer for 2 minutes until slightly thickened.

Pour the warm sauce evenly over the enchiladas. Sprinkle the remaining Monterey Jack and cheddar cheeses on top. Bake for 15 to 20 minutes, until the cheese is melted and bubbly and the edges are golden.

Remove the dish from the oven. Let it rest for 5 minutes. This helps the enchiladas set so they are easier to serve. Sprinkle fresh cilantro over the top.