Trim cores from the cabbages. Using a sharp knife, mandoline, or food processor, thinly shred green and purple cabbage until you have about 6 cups combined. Place shredded cabbage in a large mixing bowl. Add grated carrot and sliced green onion if using. Sprinkle 1 teaspoon of the salt over the cabbage, toss, and let sit 10 minutes to help draw out excess moisture. After 10 minutes, if a noticeable liquid has accumulated, drain and gently squeeze the cabbage in a clean kitchen towel or between your hands to remove excess water; return to the bowl.

Make dressing

In a medium bowl, combine mayonnaise, sour cream, apple cider vinegar, Dijon mustard, and granulated sugar. Whisk until smooth and homogenous.

Add the remaining 2 teaspoons of salt, freshly ground black pepper, and celery seed if using. Taste and adjust: the dressing should be tangy-smooth with a hint of sweetness. If you prefer brighter acidity, add the optional teaspoon of lemon juice now and whisk to incorporate.

Toss and finish

Pour the dressing over the prepared cabbage and carrot. Using tongs or two large forks, toss thoroughly so every strand of cabbage is coated. Continue tossing for 30–60 seconds to ensure even distribution.

Taste the slaw and adjust seasoning: add up to another 1/2 teaspoon salt or a pinch of sugar if needed. If slaw tastes flat, add a small splash (1/2 tsp) more vinegar or lemon juice and toss again.

Fold in chopped fresh parsley if using. Cover and refrigerate for at least 30 minutes to let flavors meld; for best texture and flavor, refrigerate 1–2 hours. Toss gently again before serving.