Heat the olive oil in a large Dutch oven over medium heat. Add the ground turkey and cook until browned, breaking it into small crumbles as it cooks. Stir in the onion, bell pepper, and garlic, then cook until the vegetables soften.
Mix in the tomato paste, chili powder, smoked paprika, cumin, oregano, and cayenne. Stir for about a minute to coat the turkey and vegetables with the spices.
Add the sweet potatoes, diced tomatoes, black beans, kidney beans, and chicken broth. Stir well, bring the mixture to a gentle boil, then reduce the heat to a steady simmer.
Cook uncovered for about 30 minutes, stirring occasionally, until the sweet potatoes are tender and the chili has thickened naturally.
Taste and adjust the seasoning with salt and black pepper. Ladle into bowls and finish with your favorite toppings before serving.