Trim any tough outer leaves from the cabbages. Cut cabbages in half, remove cores, then thinly slice to yield about 6 cups shredded green cabbage and 2 cups shredded red cabbage. Alternatively use a mandoline or food processor with a shredding disc for uniform pieces.

Shred carrots and slice aromatics

Peel and shred carrots (use box grater or food processor) to make about 1.5 cups. Thinly slice 1/4 cup red onion and thinly slice scallions. Chop parsley finely.

Combine vegetables

Place the shredded green cabbage, red cabbage, shredded carrots, sliced red onion, scallions, and chopped parsley in a large mixing bowl. Toss gently to combine so ingredients are evenly distributed.

Dressing & Assembly

Make dressing

In a medium bowl or a jar with a lid, combine 3/4 cup mayonnaise, 1/4 cup Greek yogurt, 3 tablespoons apple cider vinegar, 1 teaspoon Dijon mustard, 1 1/2 tablespoons granulated sugar, 1 teaspoon honey, 1/2 teaspoon celery seed, 1 teaspoon Kosher salt, and 1/2 teaspoon freshly ground black pepper. Whisk vigorously until smooth and sugar is dissolved (or shake the jar until emulsified). Taste and adjust seasoning—add more vinegar for tang, sugar for sweetness, or salt as needed.

Dress the slaw

Pour about three-quarters of the dressing over the prepared vegetables and toss thoroughly with tongs or two spatulas until everything is evenly coated. Add remaining dressing a little at a time until you reach your preferred creaminess (you may not need all the dressing).

Rest and chill

Cover the bowl and refrigerate the slaw for at least 30 minutes, up to 4 hours. Chilling allows flavors to meld and softens the cabbage slightly. If the slaw becomes too wet after sitting, drain briefly and re-toss with a splash more vinegar or a tablespoon of mayonnaise to adjust consistency.

Final adjustment and serve

Before serving, taste and adjust salt, pepper, or a squeeze of vinegar if brighter acidity is desired. Serve chilled as a side for sandwiches, barbecue, or salads.