Lower warmth to medium; add onion and poblanos. Cook dinner, stirring now and again, until softened, about 5 minutes. Dash in garlic, cumin, coriander, and chili powder, and prepare dinner until fragrant, 1 minute extra. Dash in canned chiles. Add rooster support to pot on the side of broth and juices, scraping up bits from the underside of the pan. Lift to a boil then decrease warmth to medium-low and simmer, partially covered, until rooster is cooked by and flavors meld, about quarter-hour.