Place shredded chicken in a bowl. Mix chicken with salt and pepper. Set aside.
Over medium heat, begin to warm the olive oil in a large pot. Add garlic to the pot, and cook for about 1 minute. Add onion, carrots, and celery to the pan. Sauté vegetables until they begin to soften (about 6 minutes).
Carefully pour all four cans of chicken broth into the large pot of vegetables. Add the can of tomatoes, can of tomatoes with jalapeños, can of drained corn, can of drained black beans, and packet of taco seasoning to the pot. Stir. Over med-high heat, slowly bring the broth mixture to a boil.
Add the chicken to the soup.
As the soup comes to a boil, cut up the tortillas into approx 1” pieces. Add tortilla pieces to the soup. Stir.
Continue to boil soup for 20 minutes, stirring about every 3-5 min. to keep ingredients from burning the bottom of the pan. (WATCH OUT: When you stir and scrape the bottom of the pan, pent up pressure will cause the mix to POP up, so stir a step or two back from the pan so you don’t get burnt).
After about 20 min. bring boiling soup down to a simmer.
Add shredded cheese to soup. Continue to simmer for 10 minutes, stirring about every 2-3 minutes. (After the cheese is added, the soup is prone to burn at the bottom so stir a lot).
Warm 1 cup heavy cream (or whole milk) BEFORE adding to the soup. Slowly add the warm heavy cream (or whole milk) to the soup.
Simmer for another 10 minutes (stirring every few minutes to keep the bottom from boiling).
Serve in a bowl w/a dollop of sour cream, some shredded cheese and broken up tortilla chips.