Discard outer leaves of your cabbage and then get to work shaving as finely as you can with a sharp knife, discarding any thick ribs as you go.
Place in a large bowl, drizzle over 1/4 C oil and toss. If the salad seems a little dry, toss through some more oil. Allow to stand for at least 15mins or up to a couple of hours.
Toss though cheese and season with s&p. Arrange on a serving platter or salad bowl and drizzle over a sparing amount of balsamic.