In a large heavy pot, heat the oil over moderately high heat. Add half the tortilla strips and cook, stirring, until pale golden, about 1 minute. Remove with a slotted spoon and drain on paper towels. Repeat with the remaining tortilla strips.
Reduce the heat to moderately low. Add the onion, garlic, and spices; cook, stirring, for 5 minutes. Add the broth, tomatoes, bay leaves, salt, cilantro leaves, if using, and one-third of the tortilla strips. Bring to a simmer. Cook, uncovered, for 30 minutes; remove the bay leaves.
In a blender, puree the soup in batches; pour it back into the pot. Add the chicken, bring the soup back to a simmer, and simmer until just cooked through, about 1 minute. Stir in the avocado.
To serve, put the remaining tortilla strips in bowls, top with the cheese, and pour in the soup. Sprinkle with the chopped cilantro, if using, and serve with the lime wedges.
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