Cut the onion into fourths. Seed and chop the poblano and jalapeño peppers. Remove husks from tomatillos and rinse well.
Add the tomatillos, onion, chiles, garlic, cumin, coriander, oregano, and cilantro to a food processor. Pulse until smooth.
Heat oil in a large stockpot or Dutch oven over medium heat. Pour in the green chile purée and cook for 10 minutes, stirring occasionally, until the mixture darkens. Season with salt and pepper.
Add the remaining chicken stock and water to the pot. Stir in the shredded chicken and drained hominy until well combined.
Bring to a gentle simmer and cook for 15–20 minutes to meld the flavors.
Ladle into bowls and serve with desired toppings: avocado, shredded cabbage, radishes, diced onion, cilantro, and lime wedges.