Heat the oil in a 6-quart, heavy bottomed pot over medium high heat until it is shimmering, then saute the onion, celery, red bell pepper, and cilantro until soft, roughly 5 minutes.
Add the minced garlic and the dried spices and stir constantly.
Add the tomato paste, mixing it in with the spices and aromatics, and cook until its color is less vibrant, roughly 2 minutes.
Slowly pour in ¼ cup to ½ cup of chicken broth to deglaze the pot. Use a wooden turner to scrape the brown bits off the bottom.
Pour in the rest of the chicken broth, green chilies, sugar, navy beans, black beans, corn, and shredded chicken. Mix well. (If you're cooking chicken breasts in the soup, add them after the thickener is added.)
Make a slurry with 2 tablespoons fine cornmeal and 3 tablespoons of warm water. Whisk to combine, then pour into the soup and stir very well. (If you're cooking the skinless, boneless chicken breasts in the soup, submerge them in the broth after stirring.)
Cover and bring to a boil, then reduce the heat to medium low and simmer for 30 minutes. During the last 15 minutes, taste and adjust seasonings, if necessary. (If using two whole skinless, boneless chicken breasts, remove after 20 minutes. Check temperature with a meat thermometer - it should read 165F when done. Allow it to cool enough to handle, 10 minutes, then shred with two forks and return to the pot.)
In a separate bowl, gradually mix a little of the hot broth into the sour cream. Whisk until it's smooth. Remove from heat, then pour in the heavy cream, tempered sour cream, and lemon juice. Stir to mix, then taste and adjust spices as desired.
Ladle the hot soup into bowls and garnish with a sprinkle of tortilla strips in the center of each bowl. Other toppings choices: diced avocado, sliced jalapeno, grated cheese, crumbled bacon, and tortilla chips instead of strips.