Trim ends of courgettes and cut into halves lengthways. Use a teaspoon to remove the pith. Paint all over with olive oil and season with salt and black pepper.
Grate some fresh parmesan sufficient to cover the flesh side of the courgettes.
Barbecue the courgettes flesh side down. Take off the grill, turn over and spoon over the parmesan. Put back on the barbecue skin side down until the parmesan is just about melted.