Wash and dry potatoes and place one at a time on a cutting board. With a sharp knife, cut crossways and vertically almost all the way down the potato, leaving a quarter inch intact. A great way to ensure you do not cut all the way through is to lay chopsticks alongside the potato.) Incise the potato every ⅛ inch, down its whole length. Place in a baking dish, insert truffle slivers as often as you dare, brush generously with melted butter, salt and pepper, sprinkle with just a few leaves of fresh thyme (too many will compete with the truffle flavor), add an optional sprinkle of Parmesan cheese or breadcrumbs, and place in the oven at 400°F for 40 minutes or so. If the potato seems to be drying out without cooking, add hot water or broth in the bottom of the dish. Cover to keep from browning too much before cooking through and through.