Using the shredder attachment on your food processor, an mandoline, a knife, shred your brussels sprouts into 1/16" shreds. You can also buy a bag of pre-shredded sprouts.
For a better texture, cut off any extra woody stems on the sprouts. For the BEST texture, use a paring knife to cut out the core of the sprout.
Combine the brussels sprouts, pomegranate, apple, pecans, cranberries and parmesan in a bowl.
Whisk together all of the dressing ingredients, pour over the salad, and toss.
Let the salad sit for about 30 minutes before serving. As it sits, the acid in the dressing will soften up the sprouts.
Serve with extra parmesan, pomegranate, and pecans.