Heat olive oil in a large pot over medium heat. Add the onion and bell pepper, sautéing until softened (about 5 minutes). Add the garlic and cook for another 30 seconds until fragrant.
Stir in the cooked turkey, diced tomatoes, tomato sauce, black beans, kidney beans, and broth. Mix well.
Add chili powder, cumin, smoked paprika, oregano, cayenne (if using), salt, and pepper. Stir to combine.
Bring the chili to a gentle boil, then reduce the heat to low. Cover and let it simmer for 20-30 minutes, stirring occasionally to prevent sticking. Add more broth if the chili becomes too thick.
Stir in lime juice to brighten the flavors. Taste and adjust seasonings as needed.
Ladle the chili into bowls and top with your choice of shredded cheese, sour cream, cilantro, or avocado. Serve with tortilla chips or crusty bread on the side.
