Heat 2 tablespoons of olive oil in a large, heavy-bottomed saucepan over medium heat. Add the diced onion and sauté until translucent, about 6 minutes.
Add the remaining olive oil and stir in the gluten-free flour blend until thickened and fragrant, about 1 minute.
Lower the heat and stir in the tomato puree, tomato paste, diced tomatoes, green chiles, chicken stock, and spices. Bring to a gentle simmer.
Submerge the chicken breasts in the soup, cover, and cook for 8 minutes or until the chicken is fully cooked.
Remove the chicken, shred it with two forks, and return it to the pot. For a vegetarian version, omit chicken entirely.
Mix in the black beans, corn, and refried beans. Stir until evenly combined.
Ladle into bowls and top with sour cream, shredded cheese, and crushed tortilla chips, if desired.