Cut the ciabatta into slices like a garlic baguette. Do not cut all the way through, it should still be lightly connected at the bottom.
Fill the individual columns alternately with tomato / mozzarella and tomato / Parma ham. Scatter basil over the filled bread, drizzle with olive oil and balsamic vinegar to taste, wrap in aluminum foil and put on the grill for about 10 minutes.