Clean and core the red cabbage, then shred it finely into 1/8-inch strips—I find using a mandoline or the shredding blade on a food processor makes this much faster and more uniform than hand shredding. Wash and thoroughly dry the shredded cabbage (excess moisture will dilute the dressing and make the slaw watery). While the cabbage drains, grate the carrots and finely chop the parsley. In a large bowl, combine the shredded cabbage, grated carrots, and chopped parsley, then season with 1/4 tsp salt and 1/4 tsp pepper.

In a small bowl or measuring cup, whisk together the mayo, sugar, lemon juice, apple cider vinegar, celery seeds, 1/4 tsp salt, and 1/4 tsp pepper until smooth and well combined. I like to let this dressing sit for a minute so the celery seeds can bloom and release their flavor into the mayo—it makes a subtle but noticeable difference in the final taste.

Pour the dressing from Step 2 over the vegetable mixture from Step 1 and toss thoroughly until all the cabbage and carrots are evenly coated. Refrigerate for at least 30 minutes before serving to allow the flavors to meld and the cabbage to soften slightly, which creates a better texture and more developed flavor.