In a caldero (stockpot), bring water to a boil. Add chicken breasts, chicken thighs, and salt and reduce the heat and simmer until chicken is tender, about 30 minutes. Remove chicken from broth, allow to cool, and then shred and set aside. Set aside the pot of chicken broth.
Heat 1 tablespoon of olive oil over high heat and fry the torn chile pieces quickly for about 1 to 2 minutes on each side. Be careful not to burn the chiles or it will have a bitter taste. Set aside.
Preheat the broiler and roast the tomatoes on a cookie sheet for about 20 minutes, turning over after 10 minutes to get all sides. Tomatoes should be mushy and slightly charred when ready. Remove only the charred pieces of skin.
Puree the roasted tomatoes, fried chiles, onion, and garlic in a blender. Put the remaining 2 tablespoons of olive oil in a deep pot over high heat. Add the blended ingredients and fry for about 5 minutes. Add the chicken broth and simmer for 30 minutes.
Add the shredded chicken (or whole chicken and thigh pieces) and simmer for another 10 minutes. Add additional salt and some black pepper to taste.
In a large skillet, heat the canola oil over medium-high heat and fry the tortilla strips until lightly browned around the edges, about 45 seconds. Transfer the strips to paper towels to drain.
In separate serving bowls set out the cubed avocados, shredded cheese, shredded cabbage, and lime wedges.
Ladle the soup into bowls and top with a handful of tortilla strips. Each person can add some cubed avocados, a squeeze of lime juice and, if desired, some shredded cheese and cabbage.
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