Heat oil in large non-stick frying pan over medium heat. Add onion and caraway seeds. Sauté until onion is softened, about 5 minutes.
Stir in cabbage, vinegar and salt. Cover. Cook just until cabbage wilts, about 4 minutes. Uncover. Increase heat to high. Add apple and honey. Cook, stirring frequently, until apple is crisp-tender and most of the liquid has evaporated, 4 to 6 minutes. Transfer to a serving plate. Top with walnuts, if used, and serve.