Start by grabbing a medium bowl and adding the mayonnaise, apple cider vinegar, Dijon mustard, sugar, celery seed, salt, and a few grinds of black pepper. Whisk everything together until it's completely smooth and creamy. This step takes less than five minutes but sets the tone for the whole dish.
Cut the green and red cabbage in half, then into wedges, and slice the wedges thinly crosswise so they fall apart into fine shreds. A sharp knife works fine, but a mandoline slicer makes this step faster and more consistent. Aim for thin, even pieces so every bite gets coated in dressing.
Slice the red onion into thin strips so its flavor spreads evenly through the slaw. Then shred the carrots on the large holes of a box grater, or julienne them into thin matchsticks. Fresh carrots give a much better crunch than pre-shredded bags sitting in the store.
Add the shredded cabbage, carrots, and onion into a large mixing bowl. Give everything a quick toss with your hands or tongs so the vegetables are evenly distributed before the dressing goes in. This makes coating everything much easier in the next step.
Pour the whisked dressing over the vegetables and toss thoroughly until every strand of cabbage is coated. Take a moment to taste and adjust the seasoning with a little extra salt or pepper if needed. The mixture should look glossy and well combined.
Cover the bowl and refrigerate the slaw for at least an hour before serving, though it's even better after a few hours or overnight. This resting time softens the cabbage slightly and lets all those tangy, sweet flavors really meld together into something special.