Roast the chilies on the grill or under the broiler, turning them a few times, until the skin is blackened. Transfer the peppers to a paper or plastic bag, seal it tightly, and set aside to steam (this makes them easier to peel).
Meanwhile, drop the tomatoes into a pan of boiling water for about 15 seconds, until the peels just begin to split open; drain and rinse the tomatoes under cold water. Peel, seed, and dice the tomatoes. Chop the onion and mince the garlic. Cut the tortillas into ½-inch-wide strips and shred the cheese. Peel, seed, and dice the roasted chilies.
Using a soup pot, heat the oil. Add the onion, chilies, and garlic, sautéing on medium heat for 5 minutes. Add the tomatoes, both kinds of broth, water, tomato juice, cumin, chili powder, pepper, and Worcestershire sauce. Bring to a boil, reduce to a simmer, and cook for 45 minutes.
4. Add the tortillas and cheese; mix well and simmer for 10 minutes.
Make sure you have extra tortilla chips and cheese. If you serve them on the side, your guests can add more to their liking.