Combine the shredded green and red cabbage with grated carrots in a large mixing bowl. I use a clear bowl so I can watch the colors blend together—it's oddly satisfying, and Lily actually got excited about helping when she could see the rainbow building.
In a separate small bowl, whisk together mayonnaise, apple cider vinegar, sugar, Dijon mustard, celery seed, salt, and black pepper until smooth. The dressing should coat the back of a spoon without dripping immediately—if it's too thin, you've added too much vinegar, so pull back next time.
Pour the dressing over the cabbage mixture and toss thoroughly, making sure every shred gets coated. This is where most people rush, but spending two minutes here means even seasoning distribution, so you won't bite into a pocket of under-dressed cabbage later.
Let the 4th of july coleslaw family recipe sit for 10 minutes before adding the shredded chicken and fresh parsley. Why the wait? The cabbage releases water and softens slightly, which helps it absorb the flavors instead of staying dense and raw-tasting.
Fold in the shredded chicken breast and chopped fresh parsley gently, using a rubber spatula rather than aggressive stirring. I learned this the hard way when I mangled the chicken into shreds smaller than confetti—it still tasted good, but the texture became mushy instead of tender.
Taste and adjust seasonings as needed—add a pinch more salt if the dressing tastes flat, or an extra splash of vinegar if it's too sweet for your family's preference. This step takes thirty seconds and prevents serving a dish you're already second-guessing.