Cut 2-3 slits in each chicken breast to allow marinade to penetrate. Place in ziplock bag with 3 tablespoons Teriyaki sauce. Leave to marinade in the refrigerator for at least 1 hour, turning occasionally.
Cook the Soba noodles according to the package directions. Drain in colander, then rinse under cold running water.
Heat greased grill pan on stove over medium-high heat. Place the chicken and cook about 5-7 minutes on each side, or until they are cooked completely through. Before removing from pan, brush the breasts with the remaining teriyaki sauce, flip and grill for 20-30 seconds to achieve a nice caramelized color. Brush the second side, flip and grill for another 20-30 seconds. Repeat glazing once or twice more to achieve desired color.
While chicken is cooking on the grill, heat sesame oil in a frying pan or wok over medium-high heat. Add the cooled Soba noodles and stir fry for 1 minute, until they are warmed through. Add in the sesame seeds, parsley, salt and pepper. Stir well until everything is combined. Remove from heat.
Serve chicken with Soba noodles. Garnish with parsley, if desired.