Preparation

• Gather the ingredients.
• In a large enameled cast-iron casserole, bring the chicken stock and water to a boil.
• Add the chicken breasts skin side down, cover, and simmer over very low heat until they're tender and cooked through, about 25 minutes.
• Skim and discard any fat from the cooking liquid and set the liquid aside.
• Transfer the chicken breasts to a cutting board or plate and, once cool enough to handle, shred the meat; discard the bones and skin.
• In a blender, combine the halved tomatillos with the quartered onion, poblanos and jalapeños, smashed garlic, chopped cilantro, and oregano. Pulse until coarsely chopped, scraping down the sides.
• With the machine on, add 1 cup of the cooking liquid and puree until smooth. Season the tomatillo puree with salt and pepper.
• In a large, deep skillet, heat the vegetable oil until shimmering. Add the tomatillo puree and cook over moderate heat, stirring occasionally, until the sauce turns a deep green, about 12 minutes.
• Pour the green sauce into the cooking liquid in the casserole. Add the hominy and bring to a simmer over moderate heat. Add the shredded chicken to the stew, season with salt and pepper, and cook just until heated through.
• Serve the pozole in deep bowls, passing the lettuce, radishes, onion, avocado, sour cream, tortilla chips, and lime wedges at the table.