Heat the oil in a large soup pot over medium heat. Add the sliced chicken breasts, chopped onion, minced garlic, ½ teaspoon cumin and salt to taste, and saute on medium heat for about 5 minutes, constantly stirring, until onion is soft and meat is no longer pink.
Cut up the cooked chicken into even thinner slices so that it looks like it's shredded.
Add chicken broth, green chili peppers, remaining cumin (½ teaspoon), 1 tablespoon chili powder, pinto beans, garbanzo beans, corn, and refried pinto beans.
Stir everything well, making sure refried pinto beans are evenly incorporated in the chili, making it thick.
If you don't have a can of refried beans, use an extra 1 can (15 oz) of pinto beans (or any white bean), pureed. The idea of adding refried beans or pureed beans is to thicken the chili. Add more chili powder if needed.
Bring to boil, make sure to stir all ingredients well together to combine flavors and spices. Reduce to simmer and cook for 15 minutes on simmer, constantly stirring, until the chili thickens.
Serve in soup bowls, garnished with shredded Cheddar or Mexican cheese, sour creams, and chopped green onion.