Shred the green cabbage into thin 1/8-inch strips and cut the purple cabbage into similarly thin strips. Grate the carrots into matchstick-sized pieces, then finely chop the fresh chives. Combine all prepared vegetables in a large bowl, tossing gently to distribute the colors evenly. I find that mixing the vegetables right after prepping them helps distribute their natural moisture evenly, which will help the dressing coat everything uniformly.

In a separate medium bowl, whisk together the mayonnaise, apple cider vinegar, Dijon mustard, and fresh lemon juice until smooth and well combined. Add the sugar, celery seeds, salt, and freshly ground black pepper, whisking until the sugar dissolves and all seasonings are evenly distributed throughout the dressing. The mustard and vinegar will help balance the richness of the mayo and brighten the overall flavor.

Pour the dressing from Step 2 over the vegetables from Step 1 and toss well, using a spatula or wooden spoon to coat every strand of cabbage and carrot evenly. Cover the bowl with plastic wrap or a lid and refrigerate for at least 1 hour before serving—this chilling time allows the vegetables to soften slightly and the flavors to meld together beautifully. I like to give it a gentle stir about halfway through chilling to ensure the dressing continues to coat everything evenly.

Just before serving, give the coleslaw a taste and adjust the seasoning as needed—add more salt, pepper, vinegar, or a squeeze of fresh lemon juice depending on your preference. Some cabbage varieties are sweeter than others, so this final check ensures the coleslaw tastes exactly how you want it.