Whisk together white wine vinegar, lemon juice, shallot, olive oil, salt and black pepper in a small bowl.
To shred the Brussel sprouts: feed the whole sprouts through the food processor tube, and use the feed tube pusher to push them down while the machine is running.
Place the shaved Brussel sprouts in a large salad bowl and drizzle it with the dressing. Give it a big toss.
If you have the time, cover it with stretch film and let it sit for 30 minutes. Doing so will help soften the sprouts and make them even more delicious.
Add in the slices of apples, cranberries, and hazelnuts. Toss to combine. Top it off with crumbled goat cheese and serve.