Preheat oven to 120°C. Melt the butter in a large non-stick frying pan over medium heat. Add apple rings; cook, turning occasionally, until tender, 10 to 12 minutes. Place in oven to keep warm.
Combine potato, carrot, onion and eggs in a large bowl. Stir in flour and salt until well combined.
Heat 2 tbsp oil in a large non-stick frying pan over medium heat. Measure a generous ¼ cup batter for each pancake and cook, 4 pancakes at a time, until well browned and crisp on the bottom, about 4 minutes. Turn pancakes over; flatten slightly with a spatula. Cook until browned, crisp and cooked through, a further 4 minutes. Drain on paper towels. Place on a baking sheet and keep warm in the oven. Make another 8 pancakes, using remaining oil as needed. Serve topped with apple rings.
Apples are a good source of vitamin C as well as potassium. Eating the peel ensures that you get the full measure of fibre. There are many apple varieties to try, including Bonza, Fuji, Pink Lady, Royal Gala, Sundowner and Braeburn.