7 cups chicken stock or low-sodium broth
2 cups water
4 chicken breast halves on the bone, with skin
1 pound tomatillos, husked and halved
1 small onion, quartered
2 poblano chiles—cored, seeded and quartered
2 jalapeños, seeded and quartered
4 large garlic cloves, smashed
1/2 cup chopped cilantro
1 tablespoon oregano leaves
Salt and freshly ground black pepper
1 tablespoon vegetable oil
Three 15-ounce cans of hominy, drained
Finely shredded iceberg lettuce, sliced radishes, chopped onion, diced avocado, sour cream, tortilla chips and lime wedges, for serving
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. Transfer the chicken breasts to a plate and shred the meat; discard the bones and skin. Skim any fat from the cooking liquid and reserve.
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 side. 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.
MAKE AHEAD The pozole verde can be prepared through Step 3 and refrigerated, covered, overnight.