In a large 6-quart Dutch oven or heavy pot, heat olive oil over medium heat. Add diced onion and cook for 4 to 5 minutes until soft and translucent. Stir in minced garlic, cumin, chili powder, oregano, and smoked paprika; cook for 1 minute until fragrant.
Pour in chicken bone broth and diced green chiles. Stir well, then nestle whole chicken breasts into the liquid. Bring to a gentle boil, reduce heat to low, cover with a tight lid, and simmer for 18 to 20 minutes until the chicken reaches 165u00b0F (74u00b0C).
Use tongs to transfer chicken breasts to a cutting board. Shred the chicken into thick, bite-sized ribbons using two forks.
In a small bowl, lightly mash 1 cup of the drained cannellini beans with a fork, then stir them back into the pot along with the remaining whole beans and sweet corn (this naturally thickens the soup).
Lower heat to medium-low. Add the cubed softened cream cheese and heavy cream. Whisk vigorously until the cream cheese melts smoothly into a velvety, creamy broth without lumps.
Return the shredded chicken to the pot along with 1/2 cup of the shredded Monterey Jack cheese and a squeeze of fresh lime juice. Simmer uncovered for 5 minutes, stirring gently, until thick and bubbling.
Ladle steaming chili into shallow ceramic soup bowls. Garnish with remaining Monterey Jack cheese, fresh cilantro, sliced jalapeu00f1os, avocado slices, and lime wedges. Serve warm with crispy tortilla chips.