With a sharp knife, cut potatoes in half lengthwise. Slice each half widthwise 6 times, but not all the way through; fan potatoes slightly.
For Baking in the Oven: Place in a shallow baking dish. Brush potatoes with 1 tablespoon butter. Sprinkle with paprika, parsley, salt and pepper. Bake, uncovered, at 350° for 50 minutes or until tender. Drizzle with remaining butter.