In a bowl combine soy sauce, chicken broth, rice wine, sugar, sesame oil, and white pepper. Dissolve cornstarch in a ¼ cup of water.
Heat a wok over medium-high. Add vegetable oil. Add broccoli and stir-fry for 2-3 minutes or until it has reached your desired tenderness. Remove from the pan and set aside. Add a little more oil to the wok if needed. Add garlic and ginger. Stir-fry for 15 seconds. Add shrimp and stir fry for 1 minute.
Add sauce mixture to the wok and bring to a boil, cook for 1 minute. Add the cornstarch and water mixture and cook while stirring until the sauce thickens. At this point, the shrimp should have turned pink and be fully cooked. Be careful not to overcook the shrimp. Add broccoli florets back into the wok, mix well. Remove from heat and serve.