Cut 20 slices in the French stick without going all the way through. Combine the oil, garlic, thyme and salt and pepper in a bowl and brush the mixture all over the cut sides and the top of the bread.
Place a slice of mozzarella in between each slice of bread. Place the stick on a double layer of foil and seal loosely. Cook on a medium-hot barbecue for 5 minutes, then open the foil out (using oven gloves, as the foil will be hot) and cook for a further 5 minutes. Serve hot.