Precook the chicken or use rotisserie chicken, shredded, and set it aside.
In a large saucepan over medium-high heat, add butter, cream cheese, heavy cream, 2 cups of Monterey Jack cheese, diced green chilies, and chicken broth. Mix until smooth and creamy.
Take a 9 x 13 casserole dish, add 2 to 3 tablespoons of shredded chicken, and shredded cheese into each tortilla. Roll them up.
Place the tortilla face down in the casserole dish to prevent unrolling.
Continue filling and placing each tortilla in the dish.
Pour the cream cheese mixture over the enchiladas and top with the remaining shredded cheese.
Bake for 20 to 22 minutes until fully warmed and the cheese is melted.
Broil for a few minutes to brown the cheese.
Sprinkle with cilantro and serve with a dollop of sour cream.
Enjoy!