Slice the peppers in half lengthways, leaving the stalks attached. Remove the seeds and brush with olive oil. Barbecue skin side down for 3-4 minutes, or until slightly charred, then turn over and barbecue for a further 2 minutes.
Lightly oil 4 pieces of foil. Place two charred pepper halves, skin side down, in the centre of each piece and put 1 tbsp of pesto in each pepper half. Divide the mozzarella between the peppers and scatter with the tomatoes and pine nuts. Drizzle with a little oil and balsamic vinegar, season and close up the foil into tightly sealed parcels.
Put the parcels on the barbecue, cover with the lid and leave to cook for 10-15 minutes, until the mozzarella has melted and the tomatoes have softened.
To serve, open the parcels, scatter with basil leaves and eat immediately.