Heat olive oil in a large pot over medium heat.
Add onion and bell pepper. Cook for 4–5 minutes until softened.
Stir in garlic and ground elk. Cook until browned, breaking the meat apart as it cooks.
Add chili powder, cumin, smoked paprika, salt, and pepper. Stir for 1 minute.
Mix in tomato paste, crushed tomatoes, kidney beans, and beef broth.
Bring to a gentle boil, then reduce heat and simmer uncovered for 30–40 minutes, stirring occasionally until thickened.
Taste and adjust seasoning. Serve hot with shredded cheese, sour cream, or green onions.