Using a large, sharp knife, and holding an ear of corn at an angle with one end resting securely on a cutting board, carefully cut down along the cob to remove the kernels. Repeat with the other ear of corn. Set the kernels in the bowl of a food processor fitted with the stainless-steel blade; reserve the cobs.
Add the garlic cloves, onion, and jalapeno to the processor. Pulse the machine on and off until the mixture is coarsely chopped, stopping once or twice to scrape down the side of the bowl with a rubber spatula. Set the mixture aside.
In a large stockpot, heat the oil over medium heat. Add the corn tortilla squares, reduce the heat slightly, and cook, stirring occasionally, until they are slightly crisp and beginning to turn golden, 3 to 5 minutes. Stir in the corn mixture and sauté, stirring, just until it's thoroughly coated with the oil but not yet browned.
Add the tomatoes, tomato paste, and cumin and continue to sauté for about 10 minutes. Stir in the chicken broth and add the corn cobs; raise the heat to high, bring the liquid to a boil, and then reduce the heat and simmer briskly until the liquid has reduced by about a third, about 30 minutes.
While the soup is simmering, prepare the garnishes: Preheat the oven or toaster oven to 350 degrees. 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.
With a slotted spoon, remove the corn cobs from the pot and discard them. Working in batches to avoid overfilling and splattering, puree the soup in a blender or food processor. Return the puree to a clean pot. Season to taste with salt and pepper.
To serve, add the chicken and avocado to the soup and reheat over low heat. Ladle the soup into 6 to 8 heated soup bowls and garnish with the baked tortilla strips, cheese, sour cream, and chopped cilantro. Serve immediately. Alternately, you can serve the garnishes in bowls at the table allowing everyone to serve themselves.