Trim outer leaves and core the cabbages. Finely shred the green and red cabbage (using a knife, mandoline, or food processor) until you have about 8 cups combined. Peel and shred or julienne the carrots. Place the shredded cabbages and carrots into a large mixing bowl. Add the sliced green onions and chopped parsley.

If using apple, core, peel and julienne it into matchstick pieces and add to the bowl. The apple adds brightness and a little crunch; toss immediately with the vegetables to prevent browning.

Make the Dressing

In a medium bowl, whisk together the mayonnaise, Greek yogurt (or sour cream), apple cider vinegar, lemon juice, granulated sugar, Dijon mustard, celery seed, salt, pepper, and honey (if using). Whisk until the sugar dissolves and the dressing is smooth and slightly thickened.

Taste the dressing and adjust seasoning: add a little more vinegar for tang, a pinch more sugar or honey for sweetness, or extra salt/pepper as needed.

Toss and Finish

Pour the dressing over the prepared vegetables. Using two large spoons or salad tongs, toss thoroughly until all cabbage and carrots are evenly coated. Make sure the dressing reaches the bottom of the bowl so every strand is dressed.

If using seeds or nuts, fold them in now to preserve crunch. For best texture and flavor, refrigerate the slaw at least 30 minutes to 1 hour before serving to let flavors meld. Give it a final toss right before serving and adjust seasoning if needed (extra salt, pepper, or a squeeze of lemon).

Storage and Serving

Serve cold as a side for sandwiches, barbecue, or fried foods. Store leftovers in an airtight container in the refrigerator for up to 3 days; the slaw will soften over time but remains flavorful.