Using a sharp knife or a mandolin, finely shred the Brussels sprouts. Put them in a large mixing bowl, add the grated carrot and toss to combine.
Whisk together the lemon zest and juice, the yuzu juice, honey, mustard and some salt and pepper. Slowly whisk in the olive oil to emulsify. Toss the vegetables with the dressing and season with some salt and pepper. Toss again with the walnuts and Pecorino and serve.