Shred the green cabbage into thin 1/8-inch strips using a sharp knife or mandoline, then grate the carrots using the large holes of a box grater, and thinly slice the red onion. Transfer all prepared vegetables to a large mixing bowl. I find that shredding the cabbage by hand gives you better control over the thickness, which makes a big difference in the final texture of the slaw.
In a separate bowl, whisk together the apple cider vinegar, Dijon mustard, honey, and extra virgin olive oil until the mixture is well emulsified and the honey is fully dissolved. Add the celery seed, sea salt, freshly ground black pepper, and smoked paprika, then whisk once more to combine all flavors evenly.
Pour the vinaigrette from Step 2 over the prepared vegetables in the bowl and toss thoroughly, making sure every piece of cabbage is coated with the dressing. Gently fold in the fresh chopped parsley. Let the slaw sit for at least 10-15 minutes before serving to allow the flavors to meld—I like to give it a quick toss halfway through so the dressing coats everything evenly.