Heat the olive oil in a large Dutch oven or heavy pot over medium heat. Add the diced onion and cook for about 5 minutes, stirring occasionally, until softened and translucent.
Add the minced garlic, cumin, oregano, coriander, kosher salt, black pepper, and cayenne pepper. Cook for about 30 seconds, stirring constantly, until fragrant.
Pour in the chicken broth. Add the chicken breasts, diced green chiles with their liquid, and one can of the drained and rinsed beans.
Bring the mixture to a gentle simmer. Partially cover the pot and cook for 15 to 18 minutes, or until the thickest part of the chicken reaches an internal temperature of 165°F.
While the chicken cooks, place the remaining can of drained beans in a bowl. Mash them with a fork or potato masher until mostly smooth.
Transfer the cooked chicken to a cutting board and shred it with two forks.
Return the shredded chicken to the pot. Stir in the mashed beans and frozen corn.
Reduce the heat to low. Add the softened cream cheese and stir gently for 3 to 5 minutes, until completely melted and the broth is smooth and creamy. Do not allow the chili to boil hard.
Remove the pot from the heat and stir in the fresh lime juice.
Let the White Chicken Chili stand for 5 minutes before serving. The broth should be creamy and lightly thickened, with tender shredded chicken and whole white beans throughout.