Thinly shred the green and red cabbage and place in a large mixing bowl.
Peel and julienne the carrots; add to the bowl with cabbage.
Thinly slice red onion if using and add to the vegetables.
In a separate bowl whisk together apple cider vinegar, sugar, Dijon mustard and celery seed.
Slowly whisk in the olive oil until the dressing is emulsified.
Season dressing with salt and pepper; taste and adjust sugar or vinegar as needed.
Pour the dressing over the shredded vegetables and toss thoroughly to coat.
Let the coleslaw sit 10–15 minutes at room temperature to soften slightly and allow flavors to begin melding.
Transfer to the refrigerator and chill at least 30 minutes for flavors to fully meld.
Just before serving, toss again and sprinkle with chopped parsley for freshness.