Heat 1 tbsp olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season the diced chicken breasts with 1/2 tsp salt and 1/4 tsp black pepper. Add chicken to the pot and cook until browned on all sides and cooked through, about 5-7 minutes. Remove chicken from the pot and set aside.

Add another 1 tbsp olive oil to the same pot. Add the chopped yellow onion and cook until softened, about 5 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the diced green chiles (undrained), rinsed and drained cannellini beans, great northern beans, and drained corn. Add the ground cumin, dried oregano, chili powder, cayenne pepper (if using), 1/2 tsp salt, and 1/4 tsp black pepper. Stir well to coat all ingredients with the spices and cook for 1-2 minutes, allowing the spices to become fragrant.

Pour in the chicken broth. Bring the mixture to a gentle simmer, then reduce heat to low, cover, and let it simmer for at least 20 minutes to allow the flavors to meld.

Stir in the heavy cream and the softened cream cheese cubes. Continue to stir gently until the cream cheese is fully melted and incorporated, creating a creamy texture.

Return the cooked chicken to the pot and stir to combine. Heat through for another 2-3 minutes. Taste and adjust seasonings as needed. Ladle the creamy white chicken chili into bowls and serve hot with your favorite toppings such as shredded Monterey Jack cheese, fresh cilantro, a dollop of sour cream or Greek yogurt, diced avocado, and tortilla chips.