Place the chicken in a large pot with enough water or broth to cover by an inch. Add half the onion, 3 garlic cloves, bay leaves, and a pinch of salt. Bring to a boil, then reduce to a simmer and cook for 20-25 minutes until tender. Transfer chicken to a plate and shred; reserve the cooking liquid.
While the chicken cooks, toast the dried chiles in a dry skillet over medium heat for about 30 seconds per side until fragrant. Transfer to a heatproof bowl, cover with hot water, and soak for 15-20 minutes until softened. Drain, discarding the soaking liquid.
Add the softened chiles to a blender with the remaining onion half, garlic, Mexican oregano, and cumin. Pour in 1 cup of the reserved cooking liquid and blend until completely smooth, adding more liquid if needed.
Pour the blended sauce through a fine mesh strainer set over a bowl, pressing with a spoon to extract all the liquid. Discard any solids left in the strainer.
Heat the oil in your Dutch oven over medium heat. Add the strained chile sauce and let it sizzle for 3-4 minutes, stirring often. Pour in the reserved cooking liquid and the 8 cups of chicken broth, stirring to combine.
Bring the broth to a gentle boil, then reduce to a simmer and cook uncovered for 20 minutes. Season with salt and pepper to taste.
Stir in the drained hominy and the shredded chicken. Simmer for another 10 minutes to warm through and combine flavors. Adjust salt if needed.
Ladle the hot pozole into bowls and serve immediately with shredded cabbage, sliced radishes, diced onion, cilantro, lime wedges, and sliced avocado on the side for everyone to add their own toppings.