Core and finely shred the green and red cabbage (use a sharp knife, mandoline, or food processor) to yield about 5 cups combined. Peel and grate the carrot(s) to make 1 cup. Thinly slice the green onions and chop the parsley if using. Transfer all vegetables to a large mixing bowl.

Lightly toss the shredded cabbages, grated carrot, green onion, and parsley to mix evenly and distribute volume so dressing can coat uniformly.

Dressing

Mix dressing

In a medium bowl, whisk together mayonnaise, yogurt (or sour cream), apple cider vinegar, Dijon mustard, and granulated sugar until smooth. Add celery seed, salt, and black pepper and whisk again to combine. Taste and adjust: add up to 1 teaspoon more sugar if you prefer sweeter slaw, or 1/2 teaspoon more vinegar for tang.

Combine dressing and slaw

Pour the dressing over the prepared vegetables. Using two large spoons or salad tongs, gently toss until all vegetables are evenly coated. Continue tossing for about 30 seconds to 1 minute, taking care not to overwork and bruise the cabbage.

Rest and chill

Cover the bowl and refrigerate at least 30 minutes to allow flavors to meld and cabbage to slightly soften. For best texture and flavor, refrigerate 2 hours. Before serving, taste and adjust seasoning with a pinch more salt or pepper if needed; give the slaw a final toss.

Serve chilled as a side. Keeps well in an airtight container in the refrigerator for 3–4 days; stir before serving as some liquid may separate.