Clean the Brussels sprouts, removing outer leaves as needed. Shred or shave by hand or by using a food processor or mandolin.
Core the apples. Do not peel. Chop apples by hand or shave them using a food processor or mandolin.
Make the dressing by combining shallots, oil, apple cider vinegar, honey, salt and pepper.
Combine Brussels sprouts and apples.
Pour dressing over Brussels sprouts and apple slaw. Toss thoroughly.
Roast and chop pecans. Combine with slaw.