Preheat the oven to 375 degrees F.
Roughly chop the hazelnuts, and then spread them out on a sheet pan and roast in the oven until golden, 5 to 7 minutes.
Wash and pat dry the Brussels sprouts and kale. Cut the Brussels sprouts in half lengthwise, through the stem. Using a sharp knife or mandoline, finely slice the Brussels sprouts crosswise to give you fine ribbons. Remove the tough stems from the kale leaves and discard. Stack the leaves up on top of one another and cut across the stem so it yields a similar shape to the shaved Brussels sprouts. Cut the sides of the apple off and cut into thin slices.
To make the vinaigrette, combine the olive oil, champagne vinegar, Dijon mustard and some salt and pepper in a bowl, whisking together until lightly emulsified. To serve, mix the Brussels sprouts, kale and apple together well in a large salad bowl. Lightly dress with the champagne vinaigrette, and then top with shaved Pecorino and chopped toasted hazelnuts.