Add chicken to a large stock pot. Cover with broth. Add bay leaves, quartered onion, garlic, salt and pepper. Bring to a boil, reduce heat to a simmer and cook partially covered until chicken is cooked through, about 30 minutes.
Transfer the chicken to a plate. Use a slotted spoon to discard onion, garlic and bay leaves. Shred the chicken meat, removing and discarding the skin and bones.
Lightly spray a jelly roll pan with cooking oil. Wash all of the peppers and cut them in half from stem to end. Remove steam, veins and seeds. (Leave some of the veins and seeds if you want the soup spicier). Place the peppers on a baking sheet cut side down. Broil for about 7-10 minutes or until the skin is charred.
Immediately place peppers in a plastic bag and tie the bag. Allow them to steam for 5-10 minutes, and then peel off their outer layer of skin (It should come off easily).
Add the peppers, cilantro and tomatillos to the blender. Add 3 fresh garlic cloves and ½ cup chopped onion. Ladle in about 1/2 cup of the broth from the chicken and blend until smooth.
Add blended sauce to the pot with the broth. Add hominy, cooked chicken, oregano, cumin, and season with additional salt and pepper, to taste. Cook for 5-10 more minutes.
To serve, ladle soup into bowls and top with a handful of thinly shredded cabbage, radishes, a lime wedge, avocado, sour cream, and tortilla strips or crushed tortilla chips.
Chicken: I suggest thighs because they're more flavorful and don't dry out as easily, but you could use chicken breast meat. Cook time for the broth may need to be reduced.Make Ahead Instructions: The soup tastes great made 2-3 days ahead of time. Add toppings just before serving.Freezing Instructions: Allow soup to cool and then freeze in a freezer-safe container for up to 3 months. Thaw overnight in the fridge and rewarm on the stove or in the slow cooker.