In a food processor fitted with a slicing blade, shred the Brussels sprouts. Next, shred the kale. Add the garlic and shallot and shred. (Alternatively, shred and mince the vegetables with a knife.) Set aside.
In a large bowl, whisk together the pecorino, olive oil, pine nuts, mustard, lemon zest and juice and salt and pepper to taste. Add in the shredded vegetables and toss well to combine. Let the salad sit for 10 minutes before serving to allow the dressing to permeate the greens.