In a 5-6 quart nonstick pan over medium heat, stir onion, garlic, cumin, oregano, chili powder, and pepper until spices are fragrant, about 1 minute. Add broth. tomatoes (including juice), and green chilies. Cover and bring to a boil over high heat.
Meanwhile, stack tortillas and cut into 1/8 inch wide strips. Add to boiling broth. Reduce heat, cover, and simmer for 15 minutes, stirring occasionally.
Rinse chicken and cut into 1/2 inch pieces. Peel the acocado, pit, and thinly slice.
Add chicken to broth and return to a boil over high heat. Reduce heat, cover, and sinner until chicken is white in center (cut to test), about 5 minutes. Stir in cilantro and salt to taste. Ladle soup into bowls, garnish with avocado, and add cheese to taste.
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