Preheat the fryer. Using a mandoline, slice the new potatoes, paper thin. Soak the potatoes for 30 minutes and drain. Pat the potatoes completely dry and place in the fryer. Fry the potatoes until golden brown, about 3 to 5 minutes. Remove the potatoes from the fryer and drain on a paper-lined plate. Season the potatoes with salt and pepper. Place the potatoes in a mixing bowl and toss with the Truffle oil and grated Parmesan cheese. Serve the potatoes immediately.