In a medium bowl, combine sliced chicken breast with 1 tablespoon soy sauce, 1 tablespoon cornstarch, salt, and black pepper. Mix well and set aside to marinate for about 15 minutes.

In a large pan or wok, heat 1 tablespoon vegetable oil over medium-high heat. Add the marinated chicken pieces and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the pan and set aside.

In the same pan, add the remaining 1 tablespoon of vegetable oil. Add minced garlic and grated ginger, sauté for about 30 seconds until fragrant.

Add sliced mushrooms and cook for 3-4 minutes until they start to soften.

Add sliced zucchinis and red bell pepper to the pan. Stir-fry for another 3-4 minutes, until the vegetables are tender-crisp.

In a small bowl, mix together 2 tablespoons soy sauce, 1 tablespoon oyster sauce, 1 tablespoon cornstarch, and 1/4 cup chicken broth. Stir until smooth.

Return the cooked chicken to the pan, and pour the prepared sauce over the chicken and vegetables. Stir well to combine, and let the sauce thicken for about 1-2 minutes.

Garnish with chopped green onions before serving. Serve the stir-fry over cooked rice or noodles.