To begin, in a small saucepan, melt butter over medium heat.
Whisk in the flour. Cook it for just a minute, until bubbly, and then whisk in the half & half and chicken broth.
Stir in the salt & pepper.
Bring it to a gentle boil and the mixture will thicken to a nice gravy.
Remove it from the heat.
In a good-sized bowl, combine the green chilies, onion, chicken, and the sauce, stir together. Cut tortillas in half and then cut those halves cross-wise into 2 inch wide strips.
In a greased 9×13 baking dish, spread about ⅓ of a cup of the mixture over the bottom, then layer half of the tortilla strips.
Spread half of the meat mixture over the tortillas.
Sprinkle with a cup or so of shredded colby-jack or cheddar cheese.
Top it with the other half of the tortillas.
Spread the remaining meat mixture over that and then sprinkle with another cup of cheese. Ready for the oven!
Bake it at 375 for 20-25 minutes, or until bubbly and golden around the edges.
Allow it to cool for a few minutes before serving.