Rinse beef, pat dry, and cut across the grain into 1/8-inch-thick slices about 3 inches long. In a small bowl, mix beef with 1/4 cup Korean marinade.
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.
Place wok over high heat; when hot, add salad 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 sesame seed.