First make the pesto. Put the basil, garlic, pine nuts, oil and salt and pepper in a food processor and process until fairly smooth. Transfer to a bowl, stir in the Parmesan and adjust the seasoning. Set aside until required.
Cut the aubergines into 1 cm (½ inch) thick slices. Season the oil with salt and pepper and brush over the aubergine slices. Heat a ridged griddle pan until hot. Add the aubergine slices, in batches if necessary, and cook for 4–5 minutes on each side until charred and tender.
Meanwhile, grill the sourdough bread.
Top the grilled bread with an aubergine slice. Spread with the pesto. Top with tomato and mozzarella slices and more pesto. Cook under a preheated hot grill for 1–2 minutes until bubbling and golden.