How to Make It
In a saucepan, combine the water, chicken, tomatoes, carrot, onion, garlic, coriander, cumin, cinnamon and the 1/2 cup of cilantro. Add a generous pinch each of salt and pepper and bring to a boil. Cover partially and simmer over moderately low heat for 30 minutes, skimming as necessary. Discard the cinnamon stick and continue simmering until the chicken is cooked through, 30 minutes longer.
Meanwhile, in a large skillet, toast the tortillas over moderate heat, turning once, until crisp in spots, 3 minutes. Cut the tortillas into thin strips.
Transfer the chicken to a plate and let cool slightly. Shred the meat; discard the skin and bones. Return the chicken to the saucepan and reheat the soup. Stir in the lime juice and season with salt and pepper. Ladle the soup into bowls. Garnish with the tortilla strips and cilantro and serve.