Heat olive oil in a large pot over medium heat. Add diced onion and cook until soft and translucent. Stir in garlic and cook briefly until fragrant. This step builds the foundation of flavor.
Pour in chicken broth and green chilies. Add cumin, paprika, oregano, coriander, cayenne, salt, and pepper. Stir well and bring the mixture to a gentle simmer. Let it cook so flavors blend together.
Drain and rinse beans. Puree one portion of the beans with some broth until smooth. Stir the puree and remaining whole beans into the pot. This creates a naturally creamy texture without heavy cream.
Add cubed Neufchatel cheese and corn. Stir until the cheese melts completely. Let it simmer gently until the chili thickens.
Add shredded chicken, lime juice, and cilantro. Stir and heat through for a few minutes. Taste and adjust seasoning before serving warm with toppings.