In a large salad bowl, empty broccoli slaw mix. Add diced apples, walnuts, onion, bacon and sliced brussel sprouts. (A food processor with a slicer or shredder attachment is a great way to prepare the brussel sprouts.) Toss well.
Using food processor, add ingredients for dressing and emulsify.
Toss again until all of the slaw is coated. Chill for 30 minutes and serve. This slaw is even better the next day!