In a large bowl, toss the chicken with about half of the salt, the pepper and the cornstarch until the chicken is well coated. Set aside.
In a small bowl mix together the oyster sauce, sesame oil, and sugar.
Heat a large skillet or wok, preferably nonstick, over medium high heat. Heat 1 tablespoon of the vegetable oil in the pan, then add the ginger and garlic and give a brief stir. Add half the chicken and stir fry until it turns white, about two minutes. Transfer the partially cooked chicken to a plate with a slotted spoon and stir-fry the rest of the chicken for two minutes. Transfer to the plate with the first batch of chicken.
Return the pan to medium high heat. Add the remaining tablespoon oil, then add the sugar snap peas and peppers and sauté for 1 minute, then add the spinach by the handful and stir-fry until it wilts, adding more as the volume goes down, until all of the spinach is added and somewhat wilted, about 4 minutes. Add the chicken broth and bring to a simmer. Add the oyster sauce mixture, and return the partially cooked chicken to the pan. Simmer, stirring occasionally for another two minutes, until the chicken is cooked through. Serve over the hot rice or quinoa.