Prepare tortilla strips: Heat about 1 inch of oil in a skillet over medium-high heat. Fry tortilla strips in batches until golden brown and crisp. Remove with a slotted spoon and drain on paper towels. Sprinkle lightly with salt. Set aside.
In a large pot or Dutch oven, combine the shredded chicken, chicken broth, diced tomatoes and green chilies, black beans, corn, onion, garlic, cumin, chili powder, oregano, salt, and pepper.
Bring the mixture to a boil, then reduce heat and simmer for 10 minutes, allowing flavors to combine.
Reduce heat to low. Stir in the cream cheese cubes until they are fully melted and the soup is smooth and creamy.
Stir in the heavy cream or milk until fully incorporated. Do not let the soup boil after adding the dairy.
Stir in the shredded cheese until melted. Taste and adjust salt and pepper if needed.
Serve the soup hot, garnished with your choice of toppings and crispy tortilla strips.
Notes
For a spicier soup, add 1/4 teaspoon of cayenne pepper with the other spices.
If you prefer a less creamy soup, reduce the amount of cream cheese and heavy cream used.
This recipe works well in a slow cooker; combine all ingredients except cream cheese and dairy, cook on low for 6 hours, then stir in cream cheese and dairy during the last 30 minutes of cooking.