Prepare the chicken: Slice the chicken breasts into thin strips. In a bowl, combine the chicken with cornstarch, salt, and black pepper. Toss until the chicken is evenly coated.
Cook the chicken: Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Add the chicken and cook until browned on all sides and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
Cook the vegetables: Add the remaining vegetable oil to the skillet and add the onion and mushrooms. Cook until the vegetables are softened, about 5 minutes.
Add the sauce: Add the garlic, soy sauce, oyster sauce, sesame oil, and water to the skillet. Stir to combine and bring to a simmer.
Thicken the sauce: Let the sauce simmer for a few minutes until it thickens slightly.
Add the chicken: Return the chicken to the skillet and stir to combine with the sauce and vegetables.
Season with black pepper: Add freshly ground black pepper to taste.
Serve: Garnish with green onions if desired and serve hot with rice or noodles.