¼ cup olive oil
1 large yellow onion, chopped
6 garlic cloves, sliced
2 teaspoons ground coriander
1 teaspoon ground cumin
½ teaspoon dried oregano (preferably Mexican), plus more for serving
1 whole organic chicken (about 4 pounds)
1½ pounds tomatillos, husked, rinsed
4 poblano chiles
3 serrano chiles
2 Cubanelle peppers (or 2 more poblanos)
2 15-ounce cans golden or white hominy, rinsed
Kosher salt, freshly ground pepper
2 cups cilantro leaves with tender stems, plus more for serving
½ small red onion, very finely chopped
Lime slices (for serving)
Heat oil in a large heavy pot or Dutch oven over medium. Cook yellow onion and garlic, stirring occasionally, until very tender, 12–15 minutes. Add coriander, cumin, and ½ tsp. oregano and cook, stirring constantly, until very fragrant, about 1 minute.
Add chicken and 12 cups water. Bring to a simmer and cook, uncovered and reducing heat as needed to maintain a very gentle simmer, until chicken is cooked through (if it isn’t completely submerged, you can turn it once or twice) and legs wiggle easily in their joints, 40–50 minutes. At this point, you can let chicken and broth cool, then chill overnight.
Meanwhile, preheat oven to 425◦. Spread tomatillos, poblano chiles, serrano chiles, and peppers on a large rimmed baking sheet. Roast, tossing once or twice, until tomatillos are tender and peppers are browned and collapsing, 30–40 minutes. Let cool.
Transfer chicken to a cutting board, reserving broth, and let cool until easy to handle. Remove meat from bones and shred into bite-size pieces. Discard bones.
Split open chiles and peppers and discard stems and seeds. Discard any skin that can be easily peeled off; otherwise, just leave it on. Reserve baking sheet. Purée tomatillos, chiles, and peppers in a blender until smooth. Stir purée into broth and bring to a simmer.
Spread hominy in an even layer on reserved baking sheet and roast, tossing once, until lightly toasted, very fragrant, and just beginning to brown around edges of baking sheet, 12–18 minutes. Scrape into pot with broth.
Simmer broth, uncovered and seasoning with salt and pepper as needed, until flavors meld and broth is rich tasting, about 20 minutes. Ladle ½ cup broth into blender. Add 2 cups cilantro and purée until smooth and very bright green, at least 1 minute. Stir chicken into broth and heat through, followed by cilantro purée. Season with salt, if needed.
Divide posole among bowls. Top with red onion and cilantro and serve with lime wedges alongside.