Heat olive oil in a large pot over medium heat.
Sauté onion and bell pepper until softened, about 3–4 minutes.
Add ground beef and cook, breaking it up, until browned. Drain excess fat if needed.
Stir in garlic, chili powder, cumin, smoked paprika, oregano, salt, and pepper. Cook 1 minute to bloom spices.
Mix in tomato paste and cook 1 minute, stirring to coat the meat and vegetables.
Pour in diced tomatoes with chiles and beef broth. Scrape the pot bottom and bring to a gentle boil.
Reduce to a simmer and cook 10 minutes to meld flavors.
Lower heat. Whisk in cream cheese until completely smooth and melted.
Stir in heavy cream and simmer gently 3–5 minutes. Finish with lime juice and adjust seasoning.
Ladle into bowls and top with cheddar, cilantro, and avocado.