Bring 4 cups of water to a boil in a large pot. Blanch broccoli florets for 30 seconds, then drain immediately and set aside.
Return water to a boil and blanch butterflied shrimp for 15 seconds. Drain immediately and set aside.
Heat wok or large skillet over high heat. Add canola oil, chopped garlic, and Shaoxing wine, stir-frying for 10 seconds until fragrant.
In a small bowl, combine warmed chicken stock, soy sauce, dark soy sauce, oyster sauce, sesame oil, sugar, and white pepper. Add this sauce mixture to the wok and bring to a boil.
Add blanched shrimp and broccoli to the wok. Stir in cornstarch slurry and cook, stirring constantly, until sauce thickens and coats the ingredients, about 1-2 minutes. Serve immediately.