Place bell pepper, onion, celery, carrots and cilantro in food processor and finely chop; set aside in a large bowl.
In a small bowl, combine garlic, chili powder, cumin and black pepper and stir into chopped vegetables. Melt 1 stick plus 2 tablespoons butter and olive oil in large pan over medium heat. Add vegetable mixture and saute, stirring often, until vegetables are transparent and lightly browned.
Finely chop the 10 ounces of tortillas in food processor and add to vegetable mixture; saute over medium heat until soft. Transfer mixture to a large pot over medium heat. Add water and chicken base, mixing until chicken base is dissolved.
In a large skillet over medium-high heat, melt remaining 1 stick butter and whisk in flour. Cook 2 to 3 minutes, while whisking, to make a roux. Add roux to soup; stir and let simmer 20 minutes. Stir in chopped tomatoes, then diced chicken; cook until heated through.
Ladle soup into bowls and sprinkle with tortilla strips and grated cheese.
Yield: 12 servings