In a bowl, combine the soy sauce, oyster sauce, cornstarch, and sesame oil. Add the sliced chicken to the mixture and let it marinate for about 10-15 minutes.
Heat 1 tablespoon of vegetable oil in a large wok or skillet over high heat.
Add the marinated chicken to the hot wok and stir-fry for about 3-4 minutes or until the chicken is cooked through and has a nice golden color. Remove the chicken from the wok and set it aside.
In the same wok, add the remaining 1 tablespoon of vegetable oil.
Add the minced garlic and ginger, and stir-fry for about 30 seconds until fragrant.
Add the sliced bell peppers, broccoli, snap peas, julienned carrots, and mushrooms to the wok. Stir-fry for 4-5 minutes or until the vegetables are tender-crisp.
Return the cooked chicken to the wok and mix it with the stir-fried vegetables.
Pour the sauce over the chicken and vegetables, and stir-fry for an additional 1-2 minutes until everything is evenly coated and heated through.
Stir in the sliced green onions and cook for an additional minute.
Serve the chicken stir-fry over cooked rice or noodles.
Garnish with additional green onions or sesame seeds if desired.