Cut the breasts into small long strips, then put them in a bowl. Add half of the hoisin sauce, and sesame oil. Mix well, then then set aside.
Peel then slice the onion and garlic.
Cut the carrot and bell pepper into small cubes.
Over high heat, stir-fry the chicken for 3-5 minutes, then remove them to a bowl, including the jus.
Heat the vegetable oil in the wok, then stir-fry the onion, ginger and garlic for a couple of minutes, then add the carrot and red pepper bits. Stir-fry for 3 minutes, then add the soy sauce and rice vinegar.
Stir, then add some water and the greens. Stir in the remaining hoisin sauce. Put a lid on and turn down the heat.
Cook for 5 minutes, then add the beansprouts and cook for 2 more minutes.
When the vegetables are tender, put back the chicken and the jus and stir-fry for one more minute.
Serve with sesame seeds scattered on top.