Assorted garnishes/toppings: avocado thinly sliced radishes, lime wedges, diced red onion, and cilantro
Heat oil in a large, heavy pot over medium heat. Add onions; cook until soft and translucent, about 5 minutes. Mix in garlic, tomato paste, chili powder, and oregano. Add 4 cups water, broth, and hominy. Stir in chicken and season with 1 teaspoon kosher salt and 1/4 teaspoon freshly ground black pepper.
Cover and bring to a boil; reduce heat to a simmer, and cook for about 30 minutes. Serve, add a squeeze of fresh lime juice, and add any other desired toppings to each individual bowl.