With a very sharp chef’s knife, cut the Brussels sprouts and radicchio crosswise in thin shreds, as you would cut cabbage for coleslaw (alternatively you can shred the Brussels sprouts in a food processor with the slicing blade!) and place them in a large bowl
In a small bowl, whisk together the lemon juice, lemon zest, olive oil, 1 teaspoon salt, and ½ teaspoon pepper. Pour enough dressing on the salad to just moisten it, reserving the rest.
Shave the Parmesan in big shards with a vegetable peeler. Add the cheese, pomegranate seeds, pine nuts, and dried cranberries to the salad and toss it carefully to avoid breaking up the cheese. Check for seasonings, add more vinaigrette, if necessary, and serve cold or at room temperature.