Wash the potatoes and set aside. Fill a large pot with water; stir in salt until it no longer dissolves and settles on the bottom. Place potatoes in the pot and bring to a boil; reduce heat and simmer until potatoes are tender but firm, about 15 minutes. Drain; cover to keep hot.
While the potatoes are cooking, melt the butter in a small pan over medium high heat, or in microwave. Serve immediately poured over potatoes.