Heat vegetable oil in a large pot over medium-high heat and stir in the ground turkey. Cook and stir until the turkey is crumbly, evenly browned, and no longer pink. Drain and discard any excess grease. Stir in the onion; cook and stir until the onion is tender, about 5 minutes.
Add the chicken broth, tomatoes, black beans, kidney beans, refried beans, garlic, chili powder, paprika, oregano, cumin, salt, and black pepper. Bring to a boil, then reduce heat to low. Cover and simmer for 30 minutes. Sprinkle each bowl with a teaspoon of Cheddar cheese, if desired.