Use a cleaver to slice beef across grain and at an angle into thin strips. Mix marinade ingredients in a medium bowl. Add beef strips; mix well. Let stand 30 minutes.
Cut each broccoli top lengthwise into 2 or 3 pieces. Dissolve cornstarch in water to make a paste; set aside. Heat 6 tablespoons oil in a wok over high heat 1 minute. Stir-fry marinated beef until very lightly browned. Remove beef, draining well over wok; set aside.
Add 1 tablespoon oil to oil left in wok. Heat 30 seconds. Stir-fry garlic 30 seconds. Add broccoli tops. Stir-fry 5 minutes. Add cornstarch paste, salt, soy sauce, chicken broth, and pepper. Remove from wok and arrange on a platter.