Slice each aubergine lengthways into 4-5mm thick strips (discard the outer strips). You need 8-10. Season with mixed herbs, salt, and pepper. Brush with oil and stand for 5 min. Char on a hot griddle for 1-2 min a side. Set aside.
Blanch the other veg in boiling water, 1 at a time: carrots for 3 min; pepper for 2; and asparagus for 1, until just tender with a slight bite. Refresh in iced water. Drain, pat dry and set aside.
Make the pesto. In a food processor, coarsely blend the garlic, tomatoes and nuts. Add the basil, cheese and oil and whizz again. Season as per taste.
Preheat the oven to 180°C/. Lay some vegetables at the end of each aubergine slice. Roll up to secure and pop in a large baking dish. Drizzle with oil and bake for 6-7 min or until hot. Serve 4 each, with the pesto.