Rinse the squash and pat them dry with a kitchen towel. Cut off both ends of each squash. Using a mandoline, a hand-held slicer, or a sharp, thin-bladed knife, cut the squash lengthwise into very thin slices. Place the squash in a large bowl and cover with a damp towel until you are ready to serve—it only takes a minute or two to finish the salad.
Just before serving, season the squash lightly with salt and pepper and toss gently. Drizzle with enough olive oil just to coat. Add the juice of half the lemon. Toss again, taste, and adjust the seasoning.
Mound the dressed squash on a platter. Tear the squash blossoms (petals only) into strips and scatter them over the salad. Discard the stamen and stem. Using a sharp vegetable peeler, shave the cheese over the platter. Serve immediately.