Place the potatoes into a large saucepan and fill with enough water to cover. Bring to a boil and cook until tender enough to pierce with a fork, about 15 minutes. Drain, cool and cut into cubes.
Heat the oil in a deep frying pan over medium heat. Add the mustard seeds; cook and stir until they start to crackle, about 2 minutes. Stir in the turmeric, curry leaves and chillies. Heat until fragrant, then add the potatoes to the pan. Cook and stir until they are coated with the seasoning. Cover with a lid and leave for about 5 minutes or until potatoes start to brown.