How to Make It
Place the chicken, 1 onion (peeled and quartered), and the celery, parsley, and pepper in a large Dutch oven or stockpot. Add 12 cups of water and bring to a boil. Cover, reduce heat, and simmer for 1 hour.
Remove the chicken from the broth, let cool, and remove the meat from the bones, shredding it into bite-size pieces; set aside.
Strain the cooking liquid and discard the solids, then pour the liquid back into the pot. Coarsely chop the remaining onions. Add the chopped onions, poblanos, jalapeños, and garlic. Bring to a boil over medium-high heat. Add the chicken, hominy, salt, cumin, chili powder, and oregano. Reduce heat to a simmer and let cook for 30 minutes.
Before serving, stir in the cilantro and lime juice. Serve warm and top with tortilla chips, chopped avocado, and sliced radishes, if desired.