Heat olive oil in a large pot over medium heat. Add diced onion and cook for 5 minutes until soft and translucent, stirring occasionally.
Add minced garlic to the pot and cook for 1 minute, stirring constantly to prevent burning.
Add chicken pieces to the pot. Season with salt, black pepper, cumin, and oregano. Cook for 5-7 minutes, stirring occasionally, until chicken turns white on the outside.
Pour in chicken broth. Add drained and rinsed white beans and diced green chilies. Stir to combine all ingredients.
Bring the mixture to a boil, then reduce heat to low. Simmer gently for 20-25 minutes, stirring every few minutes, until chicken is cooked through completely.
Add cubed cream cheese and shredded Monterey Jack cheese to the pot. Stir continuously for 3-4 minutes until both cheeses melt completely into the broth.
Taste and adjust seasonings as needed. Add more salt, pepper, or cumin to your preference.
Remove from heat and let rest for 5 minutes to thicken slightly before serving.
Serve hot in bowls with your choice of toppings such as shredded cheese, sour cream, avocado, cilantro, tortilla chips, and lime wedges.