prepare barbecue. Cut potatoes into wedges, rinse well and drained, then place in a large bowl. In a small bowl, mix basil pesto, olive oil and water. Pour over potatoes and toss to coat well. Place in a large foil pan in a single layer if possible.
Cook over indirect heat in a covered barbecue for 40 minutes, turning after 20 minutes.
Serve sprinkle with Parmesan.