Preheat the broiler to 200 degrees C. Place halved nectarines skin side down on a shallow dish or lightly greased baking tray and sprinkle with brown sugar. Grill under the broiler for 15-20 minutes till the tops are lightly charred and oozing juices. Remove and cool for 10 minutes.
Place nectarines (4 halves per person) in bowls, top with granola and yoghurt. Pour pan juices over and serve.