In a 5-quart pot, combine the chicken, 1 1/2 teaspoons salt and 8 cups water to cover. Bring to a boil, reduce to a simmer and skim any foam or impurities from the top. Add the onion, garlic, bay leaf, cilantro stems and scallion whites. Simmer, partially covered, until the chicken is tender and releases easily when pierced with a knife, 35 to 40 minutes. Transfer the chicken to a bowl to cool, about 10 minutes.
Meanwhile make the aji sauce: In a food processor, combine the scallion greens, hot sauce, tomatoes, 1/2 teaspoon salt and 1/2 cup of the cilantro leaves and pulse to a coarse sauce. Set aside. (Alternatively, the ingredients can be chopped by hand and stirred to combine.)
Add the potatoes to the soup along with 1 1/4 teaspoons salt. Cover, bring back to a simmer and simmer another 10 minutes.
Meanwhile, remove the chicken meat from the bones and shred with your hands or 2 forks (discard the bones and skin). Set aside.
Add the corn to the soup and cook until the corn and potatoes are tender when pierced with a knife, 3 to 4 minutes. Add the chicken meat back to the soup and return the soup to a simmer. Add salt if needed.
Divide the soup among 6 bowls and serve with sliced avocado, sour cream, capers, aji sauce and remaining cilantro leaves.
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