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.
Most apples are suitable both for cooking and eating, but some varieties work better in recipes than others. Apples that are suitable for cooking, such as Granny Smiths and Braeburn, are generally firmer and tarter than other varieties. They can withstand longer cooking times without disintegrating. This matters when you're baking apples or using them in a pie, but it is not so important when adding apples to a quick sauté.
One secret to successful stir-frying is to get the wok or frying pan very hot before adding the oil. This helps to prevent food from sticking. Stir-fry vegetables in small batches rather than piling them into the pan. If they're crowded, they will start to steam and lose the crisp-tender texture that is characteristic of a stir-fry.