Preheat the oven to 400 degrees F. Scrub the potatoes and pat them dry.
Place 2 chopsticks along either long side of a potato. Using a long paring or chef's knife, score the potato down to the chopsticks (the chopsticks act as a stopgap, keeping you from cutting all the way through the potato). Cut slits 1/8 inch apart all the way down the length of the potato. Repeat with the second potato.
Place the potatoes on a baking dish and brush with half the butter and sprinkle with some of the thyme and salt and pepper.
Bake for 35 to 40 minutes, brush with the remaining butter and continue baking until cooked through, about 30 minutes more. Sprinkle with more thyme and the Parmesan and bake for 5 minutes more before serving.