Precook the chicken or use rotisserie chicken, shredded. Set aside.
In a large saucepan over medium heat, add the butter, cream cheese, heavy cream, 2 cups of Monterey Jack cheese, diced green chilies, and chicken broth. Stir until smooth and creamy.
Use a 9 x 13 casserole dish, add about 2 to 3 tablespoons of shredded chicken and shredded cheese to each tortilla and roll it up. Place the tortilla face down in the casserole dish so the enchilada doesn’t unroll.
Continue this until each tortilla is filled and placed in the dish.
Pour the cream cheese sauce over the enchiladas and top with the remaining 1/2 cup of shredded cheese.
Bake for 22 minutes until the dish is completely warmed and the cheese is melted. Turn the heat up to broil for the last 3 minutes to brown the cheese.
Sprinkle with cilantro and serve with a dollop of sour cream.