1. Using a sharp knife, score each chicken breast diagonally across 3 times and rub all over with teriyaki sauce. Set aside to marinate for at least 10 minutes, or cover and let chill all day.
2. When you are ready to cook the chicken, preheat the broiler to high. Bring a pan of water to a boil, add the buckwheat noodles, and boil for 3 minutes, until soft. Alternatively, cook according to the package instructions. Drain and rinse well in cold water to stop the cooking and remove excess starch, then drain again.
3. Lightly brush the broiler rack with oil. Add the chicken breasts, skin-side up, and brush again with a little extra teriyaki suace. Broil the chicken breasts about 4 inches from the heat, brushing occasionally with extra teriyaki sauce, for 15 minutes, or until cooked through ad the juices run clear.
4. Meanwhile, heat a wok over high heat. Add the sesame oil and heat until it shimmers. Add the noodles and stir round to heat through, then stir in the sesame seeds and parsley. Finally, add salt and pepper to taste.
5. Transfer the chicken breats to plates and add a portion of noodles to each.