Preheat oven to 200ºC (390ºF). To make the nam jim, process the garlic, chilli, fish sauce, coriander root, green onion, lime juice and brown sugar in a food processor until finely chopped. Set aside.
Heat a large non-stick frying pan over medium heat. Brush chicken with oil and sprinkle with salt and pepper. Cook, skin-side down first, for 3–4 minutes each side. Place in the oven and cook for a further 5 minutes or until cooked through. To serve, slice the chicken and place in a bowl with green beans, snow peas, coriander and nam jim and toss to combine. Serves 4.