Place the vinegar, garlic, chopped tomatoes and 5 tablespoons of the olive oil in a small bowl. Mix well to combine.
Trim the asparagus spears to remove any tough, fibrous stems. Brush the asparagus with the remaining olive oil and cook on an oiled barbecue grill over medium coals 5-6 minutes until tender.
Divide the asparagus between 4 warmed serving plates. Spoon over the balsamic vinegar and tomato dressing, top with the pine nuts and parmesan slivers and sprinkle with the sea salt flakes and pepper. Serve at once with plenty of warm bread to mop up the juices.