Heat olive oil in a large Dutch oven or heavy-bottomed stockpot over medium heat. Add the diced yellow onion and sauté for 4 to 5 minutes until soft and translucent. Stir in minced garlic, diced mild green chiles, ground cumin, dried oregano, chili powder, cayenne pepper, salt, and black pepper. Cook for 60 seconds until fragrant.

Pour in the chicken broth, sweet corn, and 1 can of drained cannellini beans. Submerge the raw chicken breasts into the liquid. Bring the pot to a vigorous boil, then reduce heat to low, cover with a lid, and simmer gently for 15 to 18 minutes until chicken breasts reach an internal temperature of 165°F (74°C).

While the pot simmers, take the second can of drained cannellini beans with 1/2 cup of hot broth from the pot and puree in a small blender (or mash thoroughly with a fork until smooth). Remove cooked chicken breasts to a cutting board and shred into bite-sized ribbons using two forks.

Return the shredded chicken and the pureed bean paste to the simmering pot. Stir in the cubed softened cream cheese and heavy cream. Whisk gently on medium-low heat for 3 to 4 minutes until the cream cheese melts completely into the broth, creating a velvety, luxurious white chili. Simmer uncovered for 5 minutes to thicken.

Ladle the piping-hot creamy white chicken chili into deep bowls. Crown generously with shredded Monterey Jack cheese, fresh diced avocado, chopped cilantro, and a vibrant squeeze of fresh lime juice. Serve immediately with warm tortilla chips for scooping!