In a large mixing bowl, combine the shredded purple cabbage and shredded carrots.

In a separate bowl, whisk together the apple cider vinegar, honey, Dijon mustard, olive oil, salt, and black pepper until well combined.

Pour the dressing over the cabbage and carrots, and toss until the vegetables are well coated.

Let the slaw sit for at least 10 minutes to allow the flavors to meld before serving.