In a large mixing bowl, combine the shredded green cabbage, red cabbage, carrots, Brussels sprouts, and fennel. Mix these colorful ingredients together until well combined. Set aside.

In a small bowl, whisk together the olive oil, apple cider vinegar, honey, Dijon mustard, salt, and black pepper until smooth and creamy.

Pour the dressing over the vegetable mixture and toss thoroughly to ensure the veggies are evenly coated.

Gently fold in the pomegranate seeds and chopped walnuts into the slaw mixture, distributing them evenly.

Cover the bowl and refrigerate the slaw for at least 30 minutes to allow flavors to meld.

Before serving, give the slaw a final toss and serve on a platter or directly from the bowl.