Rinse Brussels sprouts in a colander. Pat dry with a paper towel.
Using a mandolin or a sharp knife, hold onto the stem end of each sprout and carefully shave the Brussels sprouts into very thin slices, discarding the tough stem ends. Place sprouts into a large mixing bowl.
Toss in the cranberries, apples, and goat cheese.
Gently toss in the dressing right before serving.