Using a medium saucepan, sauté onion, garlic, and green chiles in oil until soft. Add tomatoes, chicken broth, and beef bouillon. Mix in spices and simmer for 1 hour.
Cut tortillas into quarters, then into 1/2-inch strips. Fry strips in hot oil until crisp and drain.
Add fried tortilla strips to soup and simmer 10 minutes. Ladle into bowls and top with shredded cheese.
Variation: If you are using ovenproof bowls for soup, place bowls under broiler for 4–5 minutes to melt cheese.
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