Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, half of the cheddar cheese, half of the Monterey Jack cheese, garlic powder, onion powder, cumin, salt, and pepper. Mix well.
Spread a thin layer of enchilada sauce on the bottom of a 9x13 inch baking dish.
Take a tortilla and fill it with about 1/4 cup of the chicken mixture. Roll it up tightly and place it seam-side down in the baking dish. Repeat with the remaining tortillas and filling.
In a separate bowl, mix together the sour cream and cream of chicken soup until smooth. Pour this mixture over the rolled enchiladas in the baking dish.
Pour the remaining enchilada sauce over the top of the creamy mixture. Sprinkle the remaining cheddar and Monterey Jack cheeses over everything.
Bake in the preheated oven for 25-30 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it cool for a few minutes before serving. Garnish with chopped cilantro if desired.