In a large pot over medium heat, combine chicken and water. Bring to a boil, skimming scum that floats on top.
When broth clears, add onions, garlic, and salt. Lower heat, cover and continue to cook for about 10 to 15 minutes.
In a pan over medium heat, arrange tomatillos and in a single layer. Cook, turning as needed until slightly charred and softened.
Over gas flames, arrange chili pasillas and jalapeno in a single layer and roast until skins are charred. Under cold running water, remove and discard charred skin. Core and deseed peppers.
With a slotted spoon, remove onions and garlic from the pot.
In a blender, combine tomatillos, jalapeno and pasilla peppers, onions, garlic, and about 1 cup of the hot broth. Process until very smooth.
Add pureed chili mixture into the pot.
Add hominy. Continue to simmer for about 20 to 25 minutes or until chicken and hominy are tender. Season with additional salt, if needed.
Ladle into bowls and garnish with shredded cabbage, chopped onions, chopped cilantro and sliced radish. Serve hot with lime wedges and tostadas on the side.