1. Place butter in medium serving bowl and set it aside to soften while you prepare and cook potatoes.
2. Place potatoes and 1 tablespoon salt in large saucepan and fill with enough cold water to cover the potatoes by about 1 inch. Bring to boil over high heat, cover, reduce heat to medium-low, and simmer, stirring once or twice, until potatoes are just tender when pierced with thin-bladed knife or skewer, 8 to 18 minutes depending on size of potatoes. Drain potatoes.
3. Cut each potato in half. Place halved potatoes in bowl with butter and toss to coat. Season with salt and pepper to taste and toss again to blend. Serve immediately.