Warm 1 tablespoon oil in a skillet, add cabbage, onion, and green onions, stir-fry 30 seconds. Add ginger and garlic to skillet, toss with cabbage mixture, stir-fry 20 seconds. Transfer to a bowl. Warm remaining oil in same skillet, add rice. Let rice cook 3 minutes. then push to side edges of pan. Add eggs to center of pan, stir to scramble. Break eggs into pieces, stir into rice. Drizzle soy sauce over rice, add chicken, stir. Cook 2 minutes. Stir in cabbage mixture, continue cooking 1 minute.