In a large skillet or pot with a tight-fitting lid, arrange chicken in a single layer and cover with about 1 inch of water. Sprinkle in a few pinches of salt. Place on medium-high heat and bring to a boil. Cover and reduce heat to medium-low. Simmer for 10 to 15 minutes or until the internal temperature in the thickest part of the chicken reaches 165 degrees. Transfer chicken to a large bowl or cutting board and shred with two forks. Set aside. (This can be done the day before and stored in the fridge.)
In a large stock pot or dutch oven (at least 4-5 quarts), heat oil over medium heat. Add the onions and garlic and cook until translucent, about 5 to 8 minutes.
Meanwhile, add tomatoes, carrots, green pepper and jalapeno to a blender or food processor and mix until blended, but still chunky. Process longer for a smoother soup or shorter for a chunkier soup.
Once the onions are done, add all the spices to the pot and cook for one minute.
Add the shredded chicken, tomato mixture and chicken broth, corn, beans and 1/2 cup cilantro to the pot. Add an additional cup (or more) of water if you find the soup too thick for your tastes. Decrease heat slightly and simmer, partly covered, until the corn is tender and the soup is thoroughly heated, at least 30 minutes or up to an hour. Taste and add salt if necessary.
When the soup is almost ready, preheat your broiler. Place tortillas on a baking sheet (you may need to do two at a time) and put under your broiler for 1 to 2 minutes or until browned and crispy, then turn over and toast the other side. Watch closely so you don’t burn them. Cool for about 5 minutes (they get crispier as they cool) and then break into strips.
Ladle soup into a bowl and top with a handful of tortillas and a couple of tablespoons of cheese. Sprinkle with the remaining cilantro. Squeeze a wedge of lime over it just before serving.