From Heat olive oil in a large pot over medium-high heat. Add the diced yellow onion and sauté for 4 minutes. Add the minced garlic and sauté for an additional 30 seconds.
Pour in the low-sodium chicken broth, diced green chilies, cumin, paprika, oregano, coriander, cayenne pepper, and season with salt and freshly ground black pepper to taste. Bring the mixture to a boil, then reduce heat to medium-low and simmer for 15 minutes.
Drain and rinse the cannellini beans in a fine mesh strainer or colander, then measure out 1 cup. Set the whole beans aside and transfer 1 cup of the beans to a food processor along with 1/4 cup of the broth from the soup. Puree until nearly smooth.
Add the cubed Neufchatel cheese, corn, whole beans, and pureed beans to the soup and stir well. Simmer for another 5 to 10 minutes.
Stir in the shredded cooked chicken, fresh lime juice, and chopped fresh cilantro. Serve with Monterey Jack cheese, additional cilantro, sliced avocado, and tortilla chips if desired.