In a medium bowl, combine chicken with 1 tablespoon soy sauce, oyster sauce, Shaoxing wine, sesame oil, white pepper, and 1 tablespoon cornstarch. Marinate for 10 minutes.
Heat 1 tablespoon vegetable oil in a wok over high heat. Add broccoli and stir-fry for 2 minutes. Remove and set aside.
Add remaining 1 tablespoon oil to the wok. Add chicken in a single layer and sear for 1 minute, then stir-fry for 3-4 minutes until golden and cooked through.
Add garlic and ginger, stir-fry for 30 seconds.
Return broccoli to the wok. In a small bowl, whisk together chicken broth, remaining soy sauce, sugar, water, and 1 tablespoon cornstarch.
Pour sauce over chicken and broccoli. Stir-fry for 1-2 minutes until sauce thickens. Serve immediately.
Notes
For a spicier version, add chili garlic sauce. Use chicken breast for a leaner option.