Step 1

Heat ¼ cup extra-virgin olive oil in a large Dutch oven or other heavy pot over medium. Cook 1 large yellow onion, finely chopped , and 6 garlic cloves, thinly sliced , seasoning with kosher salt and stirring occasionally, until very tender, 12–15 minutes. Add 2 tsp. ground coriander , 1 tsp. ground cumin , and ½ tsp. dried oregano, preferably Mexican , and cook, stirring constantly, until very fragrant, about 1 minute.

Step 2

Place one 3½–4-lb. whole chicken in pot and pour in 12 cups water . Bring to a simmer and cook chicken, uncovered and reducing heat as needed to maintain a very gentle simmer (and turning once or twice if it isn’t completely submerged), until cooked through and legs wiggle easily in their joints, 40–50 minutes.

Step 3

Meanwhile, preheat oven to 425°. Spread out 4 poblano chiles , 2 Cubanelle peppers or 2 more poblano chiles , 3 serrano chiles , and 1½ lb. tomatillos, husks removed, rinsed , on a large rimmed baking sheet.…