Transfer the onions and garlic into a soup pot and add the chicken broth, cooked chicken, diced tomato (with liquid), corn, vegetable oil,cayenne pepper powder, basil leaves, and cilantro. Bring the mix to a quick boil, then reduce heat and simmer for 15 minutes.
Ladle soup into bowls, then garnish with tortilla chip strips (or crushed tortillas), Pepper Jack cheese, avocado slices, and/or sour cream.