How to Make It
Peel the tough outer leaves from the lemongrass and discard the top two-thirds. Mince the tender white bulb.
Season the chicken with salt and pepper. Heat the oil in a large enameled cast-iron casserole. Add the chicken, in batches if necessary, and cook over moderate heat, turning occasionally, until golden all over, about 10 minutes. Transfer the chicken to a platter.
Add the coconut milk to the casserole and bring to a boil, scraping up any browned bits from the bottom of the pan. Cook over moderately high heat until reduced to 3 cups, about 15 minutes. Stir in the curry paste and simmer over moderate heat for 5 minutes. Return the chicken to the casserole along with any accumulated juices. Add the lemongrass, lime leaves, stock and fish sauce, cover partially and simmer over low heat until the chicken is just cooked through, about 30 minutes.
Add the poblano, basil and cilantro to the chicken, cover partially and cook over low heat for 10 minutes longer. Serve right away with jasmine rice.