In a small bowl, whisk together soy sauce, oyster sauce, sesame oil, cornstarch, and water until smooth. Set aside.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Add sliced chicken and cook until golden and fully cooked. Remove chicken and set aside.
Add remaining oil to the pan. Add broccoli, bell pepper, carrot, and snap peas. Stir fry for 3–4 minutes until vegetables are crisp-tender.
Add garlic and ginger to the vegetables and cook for 30 seconds until fragrant.
Return cooked chicken to the pan. Pour in the prepared sauce and stir continuously until the sauce thickens and coats everything evenly.
Remove from heat and serve hot over rice or noodles.