Place the dried ancho and guajillo chiles in a medium bowl and cover with hot water. Let soak for 15 minutes until softened.
Drain the chiles and transfer them to a blender. Add 1 cup of chicken broth and blend until smooth. Set aside.
Heat the vegetable oil in a large pot over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Pour the chile puree into the pot and cook, stirring occasionally, for 5 minutes to deepen the flavors.
Add the remaining chicken broth, shredded chicken, drained hominy, oregano, cumin, smoked paprika, and salt to taste. Stir to combine.
Bring the soup to a boil, then reduce heat to low and simmer uncovered for 45 minutes to 1 hour, allowing flavors to meld.
Taste and adjust seasoning with additional salt if needed.
Ladle the pozole into bowls and serve with lime wedges, shredded cabbage, chopped cilantro, diced onion, avocado slices, and radish slices for garnish.