Mix together the lime juice and 3 teaspoons of the ancho chili powder in a bowl. Add chicken pieces to the marinade, cover and refrigerate for about an hour.
Preheat the oven to 350 degrees F.
Melt the ghee (or butter substitute) in a large saucepan or 3.5-quart Dutch oven on medium low, and add the red bell pepper, poblano pepper and green onions. Cook for about 7-10 minutes, then add the garlic. Stir for about 30 seconds then add in the flour, cumin, cayenne pepper and the other 2 teaspoons of ancho chile powder. Cook for about 1 minute more.
Pour in the chicken broth and cook on low until the mixture has thickened, about 2-5 minutes. Stir in the tomatoes and cover the pot. Simmer for about 15 minutes, stirring occasionally.
Meanwhile, cook the chili lime marinated chicken breast strips in a skillet on the stove top for 15-20 minutes until done. When the chicken is cooked through, let it cool and then shred it and set aside.
When the sauce is ready, remove from heat and add a squeeze of lime juice and the mayo. Stir until everything is well-combined. Add in salt and pepper to taste.
Layer 3 tortillas on top of the sauce. Cut up the tortillas to make sure the entire pan is evenly covered. Add half of the shredded cooked chicken. Then about half of the remaining sauce. Cover with 5 slices of the Chao cheese.
Next is another layer of tortillas. Then the remainder of shredded chicken. Cut the remaining 5 slices of the Chao cheese into strips and place them over the chicken (the cheese melts a lot better this way). Take the remaining sauce and pour it evenly over the chicken and cheese strips.