Preheat the oven to 350°. While the oven is preheating, toast the hazelnuts until the skins blister, about 15 minutes. Transfer the nuts to a kitchen towel and let cool, rub to remove the skins. Coarsely chop the nuts.
Remove the brown outer leaves of the brussels sprouts. Using a mandolin or knife shred the Brussel sprouts so that they're very thinly shredded.
In a bowl, whisk the olive oil, vinegar, mustard, ground garlic, lemon zest and lemon juice. Season with salt and pepper. Add the shredded brussels sprouts, pomegranate seeds and shaved cheese and toss well. Sprinkle the chopped hazelnuts on top and serve right away.