Slice the beef thinly against the grain. In a bowl, combine beef with soy sauce, Shaoxing wine (if using), sesame oil, and beaten egg white. Mix well. Add 2 tablespoons of cornstarch and mix until the beef is thoroughly coated. Let marinate for at least 15 minutes at room temperature, or up to 30 minutes in the refrigerator.

Heat 1 tablespoon of vegetable oil in a wok or large skillet over high heat. Add half of the beef in a single layer and cook for 1-2 minutes until browned on one side. Flip and cook for another minute until mostly cooked through but still slightly pink. Remove beef from the wok and set aside. Repeat with remaining beef and another tablespoon of oil, if needed.

Add broccoli and carrots to the hot wok. Stir-fry for 2-3 minutes until slightly tender-crisp. Add minced garlic and grated ginger, stir-fry for 30 seconds until fragrant.

In a small bowl, whisk together chicken broth, oyster sauce, sugar, 1 tablespoon cornstarch, and 2 tablespoons water to create a sauce slurry. Pour the sauce into the wok, stirring constantly until it thickens.

Return the cooked beef to the wok, tossing to coat with the sauce and vegetables. Cook for another 1-2 minutes until everything is heated through and the sauce clings to the beef. Serve immediately over rice.