Soak cedar planks in water for at least 1 hour.
Cut the potatoes in Hasselback fashion. I use a tool to do this (link above). You can also lay wooden spoons alongside the potato. As you cut the potato into slices, the spoons will prevent you from cutting all the way through.
Gently and carefully lightly spread the potato segments apart.
Brush the tops of the potatoes with the oil. Try to get some down inside the segments, but don't over-oil them. You want just a light coating.
Generously salt and pepper the potatoes.
Fire up your grill for direct cooking. Remove the plank from the water and place over the fire. Char on both sides then remove the plank to indirect cooking. You want a cook temperature of around 400 F.
Transfer the potatoes to the plank and cook for 30-40 minutes until a toothpick (I use a thin skewer) inserts easily into the potato. I find it's easier to poke it from the side, into the ends.
If you wish to serve with cheese melted over the top, just sprinkle the potatoes with the cheese and cook another 5 minutes.
Remove and serve.