Using a large knife, carefully scrape the kernels off the corncobs and set aside, reserving the cobs.
Using a food processor fitted with the steel blade, or a large knife, coarsely chop the garlic, onion, jalapeno pepper, and corn kernels. Reserve.
In a large soup pot, heat the oil. Add the squares of tortillas and cook over low heat until they are slightly crisp. Stir in the chopped vegetables and simmer just until the vegetables are coated with the oil. Do not brown.
Add the tomatoes, the tomato paste, and 2 teaspoons of the cumin and continue to simmer for about 10 minutes to maximize the flavor. Slowly pour in the stock, add the corncobs, and cook over low heat until the soup is reduced by one third.
Discard the corn cobs and puree the soup, in batches, in a blender or food processor until smooth. At this point, the soup can be passed through the fine strainer, if desired. Return to a clean pot and season with salt, pepper, and additional cumin to taste.
Prepare the garnish: Preheat the oven or toaster oven to 350 degrees F. Cut the tortillas into thin strips and arrange on a small baking tray. Bake until the strips are crisp, 10 to 15 minutes. Peel and dice the avocado. Cut the chicken into thin strips.
To serve, add the chicken and avocado to the soup and reheat over low heat. Ladle the soup into 6 to 8 warm soup bowls and garnish with the baked tortilla strips, Cheddar cheese, and chopped cilantro. Serve immediately.
Recipe courtesy of Wolfgang Puck, "Pizza, Pasta & More!," Random House, 2000