Cut an 8- to 10-ounce (6- to 8-in.-long) peeled potato in half lengthwise. From the center of the potato, cut even, full-length 1/16-inch or thinner slices on an Asian slicer or mandoline. You should get 15 to 20 full-size slices. Reserve extra potato for other uses.
Wrap each potato slice around a buttered cannoli tube (about 1 in. wide) or the tip of a metal pastry cone. Set, seam down, on a buttered baking sheet. Brush each slice lightly with melted butter or margarine (about 1/2 teaspoon per slice).
Bake in a 400° oven until browned, 7 to 8 minutes. Let stand until metal forms are cool enough to touch, then gently twist and slide potatoes off forms. If making ahead, seal airtight and keep at room temperature up to 1 week.