Scrub potatoes, boil in plenty of salted water, drain and peel. Bring broth and half of the vinegar to a boil and pour over the potatoes. Season with salt and pepper and soak for 30 minutes. Rinse apples, remove core, cut into quarters and sprinkle with lemon juice.
Rinse arugula and spin dry. Roast pine nuts in a dry frying pan until golden brown. Mix apple slices, arugula and pine nuts. Drizzle with remaining vinegar and oil. Add to potatoes. Serve sprinkled with Parmesan.