Scrub 4 pounds red thin-skinned potatoes (1 1/2 in. wide; cut in half if larger). Place in a 6- to 8-quart pan and add enough water to cover by 1 inch. Set over high heat and bring to a simmer. Reduce heat so water barely simmers and cook, uncovered, just until potatoes are tender when pierced, about 30 minutes. Drain.
Pour potatoes into a bowl and add 1/3 cup chopped parsley, 1/4 cup (1/8 lb.) melted butter, 1 teaspoon salt, and 1/2 teaspoon coarse- ground pepper. Mix gently to coat.