Make the dressing. Whisk together the oil, vinegar, tomato paste and lemon juice in a small bowl. Set aside.
Dry-fry the pine nuts in a hot pan until golden brown. Set aside.
Cut the stalk off the aubergine and cut it lengthwise to give 8 slices (disregarding the ends). Put the slices in a pan of boiling salted water and cook for 2 minutes. Drain and dry on kitchen paper. Cut the mozzarella into 4 slices and the tomato into 8 slices (disregarding the outer edges).
Put 2 aubergine slices in an ovenproof dish, forming an X-shape. Put a slice of tomato on top, season with salt and pepper, add a basil leaf, a slice of mozzarella, another basil leaf, then more salt and pepper, and finally another slice of tomato. Fold the edges of the aubergine around the filling to make a parcel. Repeat with the other ingredients to make 4 parcels in total. Cover and chill in the refrigerator for 20 minutes.
Brush the aubergine parcels with oil. Put the dish under a preheated hot grill and cook for about 5 minutes on each side until golden-brown. Serve 2 parcels per person, drizzled with the dressing, and scattered with the pine nuts and torn basil leaves.