Heat a broiler on high. Add poblano peppers, Anaheim peppers, tomatillos, onion and garlic to a rimmed baking sheet. Drizzle lightly with oil and cook, turning occasionally, until peppers are charred on all sides and tomatillos are softened. Transfer peppers to a bowl and cover with plastic wrap.
When the peppers have cooled, removed from bowl to a cutting board. Scrape the skins off with a knife and remove stems and seeds. Remove garlic from the skin.
Transfer skinned peppers, tomatillos, onions, and garlic to food processor. Pulse until finely chopped.
Transfer the pepper mixture to a slow cooker along with chicken broth, chicken, and spices (reserve the hominy). Cook on high for 4 to 6 hours, until the chicken is tender and cooked through.
Break up the chicken with a pair of tongs, then fold in hominy and cook another 30 minutes. Season to taste.