For the beef and marinade: In a medium bowl, combine beef with all marinade ingredients. Mix well and let stand 30 minutes.
For the sauce: In a small bowl, combine sauce ingredients and set aside.
For the stir- fry: Fill a wok halfway with water, season with salt, and bring to a boil. Add Chinese broccoli and cook until crisp-tender, about 1 minute for regular gai lan and 30 seconds for baby gai lan. Drain and set aside.
Wipe wok dry, then return to heat. Add 1 tablespoon oil and heat over high heat until smoking. Add beef, spreading it out in an even layer with a spatula, and cook without moving until lightly browned on bottom, about 1 minute. Continue to cook while stirring regularly until about halfway cooked through, about 2 minutes longer. Transfer to a bowl and set aside.
Add remaining 1 tablespoon oil to wok and heat over high heat until smoking. Add shallots and garlic and cook, stirring constantly, until softened, about 1 minute. Add Chinese broccoli and cook, stirring frequently, for 1 minute. Season with salt.
Return beef to wok and toss to combine. Stir sauce to combine. Continue to cook, stirring, until the sauce begins to thicken, about 1 minute. Transfer to a serving platter immediately and serve with white rice.