In a large pot or Dutch oven, heat olive oil over medium heat. Add the diced onion and bell pepper and sauté for 3–4 minutes until softened. Stir in the garlic and cook for another 30 seconds.
Add the shredded chicken, diced tomatoes with green chilies, green chilies (if using), chicken broth, and all the spices. Stir to combine and bring to a simmer.
Reduce heat to low. Stir in the cubed cream cheese and let it melt slowly, stirring occasionally to create a smooth texture.
Once the cream cheese is fully incorporated, add shredded cheddar and stir until melted. Pour in the heavy cream and simmer the soup gently for 5–10 minutes, allowing the flavors to meld.
Ladle the soup into bowls and top with your favorite garnishes—crushed tortilla chips, fresh cilantro, jalapeños, or a swirl of sour cream.