Return soup to pot, add remaining broth, and heat over medium heat. Stir in chicken pieces and hominy. Lower heat so that mixture simmers gently; cook 15 minutes or until hominy is tender and flavorful. When about 5 minutes are left, fold in the chicken. Taste soup, and add sea salt as needed. When soup is ready, fold in lime juice and cilantro.
Meanwhile, prep toppings. A squeeze of lime will take the spicy edge off the radishes and prevent the avocado from browning. Sprinkle with sea salt.
Ladle soup into bowls, and top with minced cilantro, avocado, radishes, and a lime wedge. If desired, finish with a pinch flaky sea salt (I used smoked sea salt here).