Using a sharp knife or the thinnest blade on a mandoline, slice each sprout thinly. Slice the apple and onion in the same manner. Combine in a large bowl.
Combine the Dijon, maple syrup, red wine vinegar, garlic and olive oil in a jar with a tight-fitting lid. Close and shake until well-combined. Pour over Brussels sprout mixture, and toss to coat. Refrigerate for at least 30 minutes. Before serving, sprinkle with toasted nuts.