Heat olive oil in a large pot over medium-high heat.
Add diced onion and sauté for about 4 minutes until softened.
Add the minced garlic and cook for 30 seconds, stirring frequently until fragrant.
Pour in the chicken broth and stir in green chilies, cumin, paprika, oregano, coriander, cayenne, salt, and pepper. Bring the mixture to a gentle boil, then reduce heat to medium-low and simmer for 15 minutes.
Meanwhile, drain and rinse the beans. Set aside 1 cup of whole beans. Puree another 1 cup of beans with 1/4 cup of broth in a food processor until almost smooth.
Add the cubed Neufchatel cheese to the pot, stirring constantly until melted and incorporated. Stir in the corn, the remaining whole beans, and the pureed beans to thicken the chili.
Simmer for an additional 5-10 minutes until the flavors meld and the chili is creamy.
Stir in the shredded chicken, fresh lime juice, and chopped cilantro. Adjust seasoning to taste.
Serve warm and garnish with extra cilantro, Monterey Jack cheese, sliced avocado, and tortilla chips, if desired.