Trim outer leaves from cabbages and remove core. Finely shred green and red cabbages using a sharp knife, mandoline, or food processor. Julienne or grate the carrots and thinly slice the red onion. Place all shredded vegetables and chopped parsley into a large mixing bowl.

For best texture, after shredding you can lightly salt the cabbage (use about 1/2 tsp of the kosher salt from the dressing list) and let it sit for 10 minutes, then squeeze out excess moisture. This step is optional — it softens cabbage and reduces excess liquid in the finished slaw.

Vinegar Dressing

Make dressing

In a medium bowl or jar, combine apple cider vinegar, water, granulated sugar, kosher salt, black pepper, dry mustard powder, and celery seed if using. Whisk or shake until the sugar and salt are fully dissolved. Slowly whisk in the oil to emulsify; the dressing will remain fairly loose compared with creamy slaws.

Adjust seasoning

Taste the dressing and adjust: add more sugar if you want it sweeter, more vinegar for more tang, or a pinch more salt and pepper to balance. Remember the vegetables will mellow the dressing slightly.

Assemble & Finish

Pour the dressing over the prepared vegetables. Using two large forks or salad tongs, toss thoroughly to coat all cabbage and carrots with dressing.

Allow the slaw to rest at room temperature for 20–30 minutes (or refrigerate for at least 1 hour) to let flavors meld. If refrigerated, give it a final toss before serving. Check seasoning and add additional salt, pepper, or a small splash of vinegar if needed.

Serve chilled or at room temperature. Keeps well in an airtight container in the refrigerator for up to 4 days; texture will soften over time.