Holding each Brussels sprout at the stem end, cut into very thin slices using a mandoline slicer. Toss in a bowl to separate layers.
Lightly crush the toasted walnuts with your hands and add to Brussels sprouts. In a small bowl whisk together oil, lemon juice, and 1/4 tsp. black pepper. Drizzle over Brussels sprouts mixture and toss to coat. Serve topped with the shaved cheese.