PLACE cedar plank in kitchen sink, large bucket or pan. Cover with water. Weigh plank down with a couple of heavy cans so it stays submerged. Soak at least 1 hour, preferably overnight.
STIR orange juice with cornstarch in a bowl until dissolved. Place shallot, butter and blueberries in a foil pie plate. Sprinkle with salt. Stir in juice mixture. Tightly cover plate with foil.
HEAT barbecue to high. Then reduce heat on one side of barbecue to medium. Place plank on medium side and pie plate with blueberries on high side. Barbecue with lid closed so plank starts to smoke, about 5 min. Then place cheese on plank. Continue grilling, with lid closed, until cheese starts to soften and berries turn saucy, about 10 min. You don’t have to stir berries. Check plank often in case it catches fire. If this happens, immediately spray with water, then reduce heat under plank.
TURN off grill and carefully remove pan with berry sauce. Stir in basil, then pour sauce into a pretty serving bowl. Using a wide spatula, place cheese on a cutting board or plate. Serve with blueberry sauce on the side and a mix of crackers, flatbread or slices of baguette.