Cut the chicken into small bite-sized cubes, roughly matching the size of the cashew nuts. Place in a bowl and mix with cornstarch, white pepper and water, then add oil to coat. Set aside.
Mix the sauce
In a small bowl, combine oyster sauce, light soy sauce, dark soy sauce, cornstarch, sugar, water, and sesame oil. Stir well and keep nearby.
Fry the cashew nuts
Add the cooking oil and cashew nuts to a cold wok or skillet (frying pan). Place over low heat and fry gently, stirring often, until the cashews turn golden. Transfer out leaving the oil in the wok.
Sear the chicken
Put the chicken in the wok. Stir fry over high heat until the pieces turn pale on the surface and are nearly cooked through. Remove from the wok and leave any oil behind.
Stir fry the vegetables
Add garlic, ginger, and onion to the wok. Stir fry until the onion begins to soften and lightly char around the edges. Return the chicken to the wok and toss for another minute to combine.
Season the dish
Give the sauce mixture a stir to loosen any cornstarch sitting at the bottom of the bowl, then pour it into the wok. Stir continuously until the sauce thickens and coats everything evenly.
Turn off the heat and fold in the fried cashew nuts. Serve immediately.