Here’s a polished, step‑by‑step version of your instructions:

1. Warm the olive oil in a large pot over medium-high heat. Add diced onion and sauté for about 4 minutes until softened. Stir in minced garlic and cook an additional 30 seconds until fragrant.
2. Pour in the chicken broth, green chilies, cumin, paprika, oregano, coriander, cayenne, salt, and pepper. Let the mixture come to a gentle boil, then lower the heat to medium-low. Simmer uncovered for 15 minutes to allow the flavors to develop.
3. As the soup cooks, set aside one can of beans to use whole. Place the second can (about 1 cup) into a food processor along with ¼ cup of the hot broth. Puree until mostly smooth—this adds a creamy thickness.
4. Mix in the Neufchâtel, corn, reserved whole beans, and the blended beans. Simmer for another 5–10 minutes until everything is heated through and the cheese has melted.
5. Remove from heat and stir in the shredded chicken, lime juice, and chopped cilantro. Give it a final taste and adjust seasoning as needed.
6. Ladle into bowls and garnish with extra cilantro. Optional toppings like tortilla chips, Monterey Jack cheese, and avocado slices add flair at serving.