Using the fluted blade of the French mandoline, cut the potato into 1/8-inch-thick slices, creating the waffle pattern by turning the potato a quarter-turn after each slice. Transfer potato slices to a bowl of cool water to prevent discoloration.
In a heavy-bottomed Dutch oven or high-sided stockpot, heat the oil until a deep-frying thermometer registers 300 degrees. Remove about 12 potato slices from the water, place on a clean kitchen towel or paper towel, and thoroughly pat dry. Carefully slip the potato slices into the oil, and fry, moving slices with tongs or a slotted spoon, until golden, 1 to 2 minutes. Transfer chips to paper towels to drain, and sprinkle with salt. Repeat until all the potato slices are fried. Let cool. The chips can be made in advance and kept in an airtight container at room temperature up to 4 days. In very humid weather, the chips may absorb moisture and soften. To re-crisp them, heat in a warm oven. Under these conditions, they are best made just 1 day in advance.