Sauté Aromatics: Heat olive oil in a large pot over medium-high heat. Add diced onion and sauté for 4 minutes. Add garlic and sauté for 30 seconds longer.
Build the Base: Add chicken broth, green chilies, cumin, paprika, oregano, coriander, cayenne pepper, and season with salt and pepper to taste. Bring the mixture to a boil, then reduce heat to medium-low and simmer for 15 minutes.
Prepare the Beans: Drain and rinse the beans in a fine mesh strainer. Measure out 1 cup of beans, set the whole beans aside, and transfer the 1 cup to a food processor along with 1/4 cup of broth from the soup. Puree until nearly smooth.**
Combine Ingredients: Add Neufchatel cheese, corn, whole beans, and pureed beans to the soup. Stir well and simmer for an additional 5-10 minutes.
Finish the Chili: Stir in shredded chicken, fresh lime juice, and chopped cilantro. Serve warm with optional toppings such as Monterrey Jack cheese, avocado slices, tortilla chips, and additional cilantro.