Warm the olive oil in a large pot over medium-high heat. Add the onion and sauté until just tender, about 4 minutes. Stir in the garlic and cook for 30 seconds more.
Pour in the chicken broth and add the diced green chiles. Season with the cumin, paprika, oregano, coriander, cayenne, plus salt and pepper to taste. Bring just to a boil, then reduce the heat to medium-low and simmer for 15 minutes.
Drain and rinse the cannellini beans. Measure out 1 cup of the beans and set the remainder aside. In a food processor, combine the measured 1 cup beans with 1/4 cup hot broth from the pot and process until nearly smooth.
Stir the Neufchâtel into the pot along with the corn, the reserved whole beans, and the bean purée. Simmer gently for 5 to 10 minutes.
Fold in the shredded chicken, lime juice, and cilantro. Serve hot with Monterey Jack, extra cilantro, avocado slices, and tortilla chips if desired.