Warm the olive oil in a large pot over medium-high heat, then add the diced onion and cook for 4 minutes. The onion should look softened and translucent around the edges, not deeply browned.
Stir in the garlic, cumin, paprika, oregano, coriander, and cayenne pepper, then cook briefly before adding the broth and green chilies; season with salt and black pepper to taste. Your kitchen will smell warm and earthy as the spices bloom, which helps them taste fuller in the finished chili.
Bring the pot just to a boil, then lower the heat to medium-low and simmer for 15 minutes. The broth should settle into a gentle bubble so the flavors can blend without reducing too fast.
Drain and rinse the beans, measure out 1 cup, and blend that portion with 1/4 cup broth from the pot until nearly smooth. This mixture should look thick and creamy, with only a little texture left.
Stir the softened Neufchatel into the chili along with the corn, the remaining whole beans, and the puréed beans, then simmer 5 to 10 minutes more. By the end, the chili should look slightly thicker and creamy enough to coat the back of a spoon.
Stir in the shredded chicken, lime juice, and cilantro, then serve with tortilla chips or strips, monterrey jack cheese, and sliced avocado if desired. The final flavor should taste rich first, then bright and fresh right at the end.