In a large pot, combine 10 cups water, the quartered onion, cilantro stems, dried chilies, coriander seeds, cumin seeds and ½ teaspoon salt. Cut off and discard the top third of the garlic head, leaving the cloves intact, and add to the pot. Cover and bring to a boil, then simmer for 10 minutes. Add the chicken and return to a boil. Reduce the heat to medium-low and cook, partially covered, for 30 minutes, maintaining a gentle simmer.

Meanwhile, heat the broiler to high with a rack positioned about 6 inches from the element. Arrange the poblanos and jalapeños on a broiler-safe rimmed baking sheet and broil, turning frequently, until evenly blackened and blistered, 10 to 12 minutes. Transfer to a bowl, cover tightly and set aside. Chop the cilantro leaves and set aside.

Peel, stem and seed the charred chilies, then roughly chop and add to a food processor along with the tomatillos. Pulse until coarsely chopped, 6 to 8 pulses.

Transfer the chicken and garlic head to a plate and let cool. Strain the broth, discarding the solids. Wipe out the pot. Add the oil, chopped onion and ¼ teaspoon salt. Cook over medium-high, stirring occasionally, until softened and beginning to brown, 7 to 9 minutes. Add the ground coriander, cumin and oregano and cook, stirring constantly, for about 1 minute. Add the tomatillo-chili mixture and cook, stirring frequently and scraping up any browned bits, until most of the moisture has evaporated, about 5 minutes. Add the broth and bring to a boil.

Shred the chicken into bite-size pieces, discarding the skin, bones and cartilage. Using tongs, squeeze the garlic cloves from the head into the soup. Add the chicken and hominy. Return to a simmer and cook until heated through, about 5 minutes. Stir in ½ cup of the chopped cilantro, then taste and season with salt. Serve, topping individual portions with pumpkin seeds, additional chopped cilantro and sour cream (if using). Pass lime wedges on the side.