Wrap each potato in a double layer of foil and either place them on the flat plate of a gas barbecue or, using barbecue tongs, set them in among the heated coals of a charcoal barbecue, allowing some of the coals to cover the potatoes. Bake for 40 minutes.
Meanwhile, make the butter. Place the butter, mustard, thyme and some pepper in a bowl and mash with a fork until evenly mixed. Set aside.
Remove the potatoes from the barbecue (again using tongs) and carefully remove the foil using oven gloves. Cut the potatoes in half and serve topped with the butter.