Whisk vinegar, sugar, and salt; toss with cucumber, onions, and sesame oil; chill 10 minutes.
Heat oil; cook garlic, ginger, and beef until browned, 5 minutes; drain.
Stir in brown sugar, soy sauce, and gochujang; cook 2 minutes.
Add broccoli slaw and green onions; cook 1–2 minutes.
Serve beef over rice topped with pickled cucumbers.