Squeeze half a lemon into a bowl of cold water.
Clean and trim the artichokes, then slice in half lengthwise. Rub the cut artichokes into half a lemon. Scrape out the choke, then slice lengthwise into as small a slice as possible. Put the slices in the lemon water until you're ready to eat. (You can do this ahead of time.)
Drain and dry the lemon slices and put them in your serving bowl. Pour the olive oil over the slices, and then squeeze in the juice of the remaining lemon. Toss well, seasoning to taste with salt. Add the shaved cheese and serve.