Cut the chicken into 2 × ¼-inch slices. In a bowl, mix the salt, pepper, and 1 teaspoon cornstarch. Stir in the chicken.

Cut off and discard the stems from the mushrooms. Rinse the mushroom caps in cold water, pat dry, and cut into ½-inch strips.

Remove the strings from the snow peas. Bring a small pot of water to a boil, place the snow peas in the boiling water, and return to boiling. Immediately remove from the heat; drain. Immediately rinse with cold water; drain. In a small bowl, mix 2 teaspoons water, the remaining 2 teaspoons cornstarch, the oyster sauce, and sugar.

Heat a wok or nonstick pan over high heat. Add the vegetable oil and chicken and cook and stir until the chicken turns white, about 2 minutes. Add the ginger, garlic, and mushrooms and stir and cook for 1 minute. Add the chicken broth, cover, and cook for 1 minute. Stir in the cornstarch mixture; cook and stir until thickened. Add the snow peas; stir and cook for 30 seconds. Remove to a heated platter and garnish with the shredded green onion.