Boil the chicken breasts until cooked through (if need be), then let cool before shredding.
Preheat the oven to 350.
Prepare the sauce (while the chicken is cooking) by melting the butter in a large saucepan. Once melted, stir in the chopped green bell pepper, red bell pepper and onion. Let cook in the butter for about 3 minutes. Add the seasonings and then the flour. Mix well until flour is pasty but mixed in. Slowly pour in the chicken stock, stirring while pouring to keep the flour from clumping. Over medium heat, let the sauce bubble and thicken.
Once thickened, stir in the sour cream, diced tomatoes with green chiles and the cilantro. Add the cooked and shredded chicken and 1 cup of the shredded cheese. Bring to bubbling, then turn down on low until ready to assemble the layered enchiladas.
Add 6 corn tortillas to the bottom of the baking dish. Spoon half of the chicken-sour cream sauce over the tortillas. Add another layer of 6 tortillas and then spoon the remaining sauce on top. Add the other cup of shredded cheese on top.
Bake at 350 for 25-30 minutes, or until cheese has melted on top. Serve King Ranch Chicken Enchiladas with side salad.