In a large soup pot, heat the olive oil over medium-low heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes. Add minced garlic and cook for an additional minute.

Stir in oregano, cumin, salt, pepper, paprika, and cayenne pepper. Sauté the mixture for 1 minute until aromatic.

Pour in chicken stock and add green chiles. Stir-and scrape any flavorful bits from the bottom. Increase heat to bring to a low boil for about 2 minutes.

Reduce heat to maintain a gentle simmer, cooking uncovered for about 25 minutes.

Lower the heat further and add the cream and cream cheese. Stir until melted, then add shredded chicken. Warm through for about 10-15 minutes.

Adjust seasoning if needed, then serve hot garnished with your choice of toppings.