Trim the ends off 1 pound Brussels sprouts. Using a sharp knife OR using the thinest blade on a mandoline slicer (and a no-cut glove) slice each sprout thinly. Slice 1 medium tart apple and 1 medium red onion in the same manner. Combine in a large bowl.
Toast 1 cup chopped walnuts in a skillet over medium-high heat, stirring frequently, until fragrant and lightly browned, about two minutes. Add to the Brussels sprout mixture. Toss to combine.
Combine the vinaigrette ingredients into a jar with a tight-fighting lid. Close the lid and shake until well-combined. Pour over the Brussels sprout mixture, and toss to coat. Refrigerate for at least 30 minutes before serving.