Trim the ends off the Brussels sprouts, and remove the outer leaves, especially if they are damaged or dirty. Place the sprouts in a bowl of cool water and let them soak for a few minutes.
Put the Brussels sprouts in a food processor, and process using the shredding blade at high speed until finely chopped.
Remove the chopped sprouts, and place in a large bowl. Using the shredding attachment, use the food processor to shred the carrots. Place in the large bowl.
Add the diced apple, cranberries, and pepitas to the sprouts and carrots.
In a small bowl, combine the dressing ingredients. Whisk together with a fork.
Pour the dressing over the salad ingredients. Stir well. Season with more salt and pepper if desired.
Notes
Store leftover slaw in the refrigerator - it should stay fresh for about 4 days. It will be crispiest on the first day, but it should still taste good after that. If it starts to lose flavor, you can add a little more dressing to liven it up again.