Preheat oven to 350 degrees. Spray a 9X13 inch baking dish with nonstick cooking spray.
In a large skillet, saute onion and garlic until soft and translucent. Add the cumin, oregano and black pepper and cook for about 1 minute, stirring constantly. Add chilies, including the juice, both soups, and chicken broth and whisk until mixture is combined and smooth.
Pour 1/2 cup of the sauce on the bottom of the baking dish. Spread 1/3 flat of tortillas in a flat layer on top, 1/3 of the remaining sauce, 1/2 the chicken, 1/3 of the cheese.
Continue with the second layer of 1/3 of tortillas, 1/3 of the sauce, the remainder of the chicken, 1/3 of the cheese.
Finish with the third and last layer with the remaining the tortillas, the sauce, and the cheese.
Bake in the preheated oven, uncovered, for 35-45 minutes or until heated through the center and sauce is bubbly.