Scrub or scrape the potatoes and dry them well. Melt the butter in a pan wide enough to take all the potatoes in one layer. Add the potatoes and stir, turning them so that they are well coated with butter.
Cover the pan with a lid and allow the potatoes to cook gently over low heat for 20–30 minutes. Shake the pan occasionally until the potatoes are crisp and golden outside and soft inside. Draw off the heat, sprinkle with salt (see note) and serve.