Begin with a large pot. Saute the vegetables and chile briefly in about 2 tablespoons of vegetable oil over medium-high heat for 3 to 4 minutes. When the vegetables are limp, add the broth and add the garlic and cumin and bring to a boil. Reduce heat, add chicken, and simmer for 10 to 15 minutes.
Meanwhile (or beforehand), fry the corn tortilla strips in 350 degree F oil for 2 minutes until crispy. Drain well on paper towels.
With the cornstarch in a cup-sized container, mix as little cold water as possible to form a thin paste. Bring the soup back up to a boil; stir with 1 hand and pour the slurry in slowly with the other. Continue to cook on high heat for a minute, then reduce to low. The soup will look cloudy at first but will clear up and thicken slightly. Remove from heat.
Add cilantro and lime juice. Fill 8 to 12 cups or bowls about 1/4 full of crushed tortilla chips. Ladle soup on top. Place a handful of strips on top of each and serve. This soup (without the tortillas) keeps well for 3 to 4 days refrigerated. Tortillas will also keep well for a few days if sealed well and stored at room temperature. In moist climates they may require re-crisping in a 350 degree F oven for a few minutes.
This "machaca" style cooked meat is very versatile: use in tacos, enchiladas, soup, nachos, burritos, etc. Basically a process of braising, the meat and all ingredients are put together in a large pot and brought slowly to a boil. Reduce the heat and simmer for 1 to 1 1/2 hours. If you desire, you can bake all of this in a covered dish in a 350 degree F. oven for about 3 hours for the same results. The meat should be tender to the point where it begins to shred...some of it may require quick chopping. You may want to reserve the liquid for use in soups, etc. Use the cooked meat in your dish right away or refrigerate for up to 3 days.
Yield: 4 to 8 servings