To shave Brussels sprouts, trim the ends and halve. With a cut side down, make thin slices with your knife across the Brussels sprout to shred. You can also shred them on the blade of your food processor or buy them pre-shaved.
In a large bowl, combine all ingredients and season to taste. Transfer to a serving platter and garnish with more olive oil and Parm. Serve immediately or let chill for softened Brussels. Will keep in an airtight container for 1 day.