Remove any tough outer leaves from the cabbages. Quarter each cabbage, remove core, and finely shred using a sharp knife, mandoline set to a thin setting, or a food processor with the shredding disk. Place shredded cabbages in a large mixing bowl.

Peel and grate or julienne the carrots. Thinly slice the red onion into half-moons. Add carrots, sliced onion, and chopped parsley to the bowl with the shredded cabbage.

Optional — reduce moisture and soften: sprinkle 1/4 teaspoon of salt over the vegetables and toss. Let sit 10 minutes, then gently squeeze out excess liquid in handfuls or with a clean kitchen towel or mesh strainer. Return vegetables to the mixing bowl.

Dressing

Mix dressing

In a medium bowl, combine mayonnaise, plain yogurt (or sour cream), apple cider vinegar, Dijon mustard, sugar, celery seed, kosher salt, black pepper, and lemon juice if using. Whisk until smooth and sugar is dissolved. Taste and adjust seasoning — add more vinegar for tang, more sugar for sweetness, or more salt and pepper as needed.

If you prefer a thinner dressing, whisk in 1 to 2 teaspoons of water or additional lemon juice until you reach desired consistency.

Combine & Finish

Pour the dressing over the prepared vegetables. Using clean hands or two large spoons, toss thoroughly until all vegetables are evenly coated. Make sure to scrape the bowl to incorporate any dressing left behind.

Let the coleslaw rest in the refrigerator for at least 30 minutes to allow flavors to meld. For best flavor and texture, chill 1–2 hours. If the slaw releases liquid after chilling, briefly toss again and, if desired, drain off a little excess liquid before serving.

Taste before serving and adjust seasoning (salt, pepper, or a splash of vinegar) if necessary. Garnish with a little extra chopped parsley or a sprinkle of celery seed, if desired.