Heat oil in a large pot over medium heat. Add onion and cook 3–4 minutes until softened.
Stir in garlic and bell pepper; cook 2–3 minutes until fragrant and slightly tender.
Add tomato paste and cook about 30 seconds, stirring to coat the veggies.
Pour in diced tomatoes (with juices) and stir well.
Add chili powder, cumin, smoked paprika, oregano, salt, and black pepper; stir and let toast for 1 minute.
Add chicken broth and bring to a gentle simmer.
Stir in shredded cooked chicken and simmer uncovered 10–15 minutes.
(Optional) Reduce heat to low and stir in cream cheese until melted smooth, or stir in heavy cream.
Turn off heat and stir in lime juice.
Ladle into bowls and add desired toppings before serving.