In a bowl, coat the beef strips with 1 tablespoon of soy sauce and 1 tablespoon of Shaoxing wine (or dry sherry). Let it marinate for 30 minutes at room temperature, or refrigerate for an hour.

While the beef is marinating, mix the remaining 3 tablespoons of soy sauce with the cornstarch until smooth. Stir in the remaining Shaoxing wine (or dry sherry), oyster sauce, chicken broth, sugar, and sesame oil until well combined. Set this sauce mixture aside.

In a separate bowl, combine the scallion whites with the minced garlic and ginger, and set aside.

Heat 1 tablespoon of oil in a large sauté pan or wok over high heat until it begins to smoke. Add the broccoli florets and stir-fry for about 30 seconds. Pour in the water, cover the pan, and reduce the heat to medium. Allow the broccoli to steam until tender-crisp, around 2 minutes. Remove from the pan and set aside on a paper towel-lined plate.

Wipe the pan dry, return it to high heat, and add another tablespoon of oil. Once the oil is smoking hot, add half of the beef strips, ensuring they form a single layer. Sear the beef without stirring for about 1½ minutes, then cook, stirring occasionally, until the beef is lightly browned but still slightly pink in some areas, approximately 30 seconds more. Remove the beef from the pan and set it aside.

Add the final tablespoon of oil to the pan, heat until smoking, and repeat the process with the remaining beef. After searing the second batch of beef, add the scallion, garlic, and ginger mixture. Stir constantly for about 30 seconds, until aromatic.

Return the first batch of beef and the broccoli to the pan, along with the reserved sauce and scallion greens. Bring the mixture to a boil, stirring and tossing continuously, until the sauce thickens slightly, about 45 seconds. Transfer to a serving dish and serve with rice.