Salad: Thinly shave Brussels sprouts and apple using a mandolin or food processor. Roughly grate cauliflower using a box grater or food processor. In a large bowl, toss together shaved sprouts, apple, cauliflower, and cranberries.
Dressing: Whisk together all dressing ingredients.
Serve: Drizzle dressing over salad and toss together. Serve room temperature or chilled.