Rinse the courgette and aubergine and cut into 1½ cm slices. Brush each slice with oil. Cut the mozzarella into 1 cm slices.
Rinse and chop the rosemary finely.
At the barbecue:
Prepare the barbecue for direct heat – approx. 180°C. When using a charcoal barbecue you need 1/3 of a chimney starter of lit Weber briquettes to reach this temperature.
Grill the courgette and aubergine slices for 3 min. on each side so they get sear marks. Remove the slices from the barbecue.
Layer the grilled slices of courgette and aubergine with the mozzarella: 1 slice of aubergine, 1 slice mozzarella, 1 slice courgette, 1 slice mozzarella and finish off with 1 slice aubergine.
Place the vegetable basket containing the small ‘towers’ on the grate and grill for approx. 3-4 min. until the cheese is melted. Sprinkle with fresh rosemary and season with salt and pepper before serving.