• Preheat your oven to 400F. Line a rimmed baking sheet with a Silpat, use a nonstick baking sheet or a medium-sized baking dish.
• Cut off the two ends of one potato and reserve them. Trim the 4 sides of the potato to form an even brick. Slice of potato about 1/8 inch thick on a mandoline, keeping the slices in order if you can (just like a line of shingled dominoes). Hold the stack of potato slices in the palm of one hand and use the other to shape them back into a brick, as you would a deck of cards. Lay the stack on its side on the baking sheet and put the reserved potato ends, cut side down at either end keep the stack aligned. Then, with the palm of your hand, angle slices slightly to resemble a line of dominoes that has tilted over. Adjust the end pieces to keep the stack and shape, and align the slices if necessary.
• Dot the top and sides with pieces of the clarified butter. Sprinkle with salt to taste. Repeat with the remaining potatoes, keeping the stacks at least 2 inches apart.
• Bake for 40 minutes, or until the potatoes are browned on the edges and tender in the middle when tested with a skewer. Serve immediately.

To Make the Clarified Butter:

• Slowly melt the butter in a heavy small saucepan over medium low heat. Do not stir. Remove from the heat, and carefully spoon off all of the foam from the top. Pour the clear liquid butter through a fine mesh strainer lined with cheesecloth, leaving behind the solids in the pan. Once cool, the clarified butter can be refrigerated for weeks.