For the Marinade: In a small bowl, mix soy sauce, sugar, minced garlic, fresh ginger and the toasted sesame oil.
To Complete the Dish: Cut beef across the grain into 1/8-inch-thick slices about 3 inches long. (Keeping the slices thin makes for a better dish.) In a small bowl, mix beef with 1/4 cup Korean marinade.
In the meantime, remove and discard bean stem ends and strings. Cut beans diagonally in 3-inch lengths. Cut carrot into matchstick-size pieces about 3 inches long.
In a 14-inch wok or 12-inch frying pan over high heat, mix 1/2 cup water, beans, and carrot. Cover and stir occasionally just until tender to bite, about 3 minutes. Drain; immerse in cold water. Drain when cool. In a bowl, mix with vinegar, sesame oil, sugar and salt to taste. Set aside.
Place wok over high heat; when hot, add oil. Add beef with liquid in bowl; stir until meat is no longer pink, about 2 minutes. Add remaining marinade and broth to pan; stir until boiling.
Scoop rice into bowls; add beef and sauce, then vegetables and seasonings. Sprinkle with onions and toasted sesame seed.