Return the pot to medium and add the jalapeños, garlic, cilantro stems and the charred peppers and shallots.
Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the broth and bring to a boil over medium-high, scraping up any browned bits.
Return the chicken to the pot, nestling the pieces in the liquid, then add any accumulated juices.
Bring to a simmer, then cover, reduce to low and simmer, stirring occasionally, until a skewer inserted into the largest thigh meets no resistance, 35 to 40 minutes.