Separate the leaves of the lettuce, discarding any tough or discolored outer ones. Wash and dry thoroughly. Tear large leaves in half, and place in a salad bowl. Slice Parmesan into very thin shavings, using a vegetable peeler or specialty slicer. Scatter cheese over lettuce. Sprinkle with balsamic vinegar and salt, and toss well. Drizzle with oil and toss again. Serve immediately.