King Ranch Chicken is implanted in Texans at birth. They have taken a broad foot in what they are made of. They go from Tex-Mex parts to adding mushrooms to flour tortillas. No doubt different regions in Texas plus the Mother who made your King Ranch isn't exactly etched in stone. The one I've made is with grilled chicken which isn't exactly how I had it as a kid, but the rest is.
Add onions, bell pepper, garlic, salt, and pepper.
Cook till translucent and sprinkle in flour.
Stir until flour is incorporated well.
Pour in chicken stock, cream, and poblanos.
Stir until the mixture begins to simmer.
Add 1 1/2 cup of shredded cheese and stir until melted.
Add grilled chicken, mix in and turn off heat.
In a Pyrex rub some butter in it.
Add a light layer of the mixture.
Layer corn tortillas over the mixture.
Add a good bit of the mixture over tortillas reserving about a cup.
One more layer of tortillas on the mixture.
Spread remaining cup of mixture on top.
Sprinkle remaining 1/2 cup of cheese over top.
Place in oven for 45 minutes or until bubbling cheese.
Pull, let cool, and get after it!
You don’t have to grill the chicken but I recommend you at least brine in like I did in this recipe. (3 tbs salt 1 quart of water) https://texasbutter.com/cajun-chicken-melt/ Used Biddy to season chicken but that’s flexible.