1. Prepare the Red Cabbage:
* Remove any tough or wilted outer leaves from the red cabbage.
* Cut the cabbage in half through the core, then cut each half in half again to make quarters.
* Carefully cut out the hard white core from each quarter.
* Place a cabbage quarter cut-side down on your cutting board. Using a sharp knife, slice the cabbage as thinly as possible. Alternatively, you can use a mandoline slicer (with extreme caution and a safety guard) or the shredding disk of a food processor.
* Place the shredded red cabbage into a large mixing bowl.

2. Prepare the Carrots (and Onion if using):
* Peel the carrots. Grate them using a box grater or the grating disk of a food processor.
* Add the grated carrots to the bowl with the red cabbage.
* If using red onion, slice it very thinly and add it to the bowl. For a milder onion flavor, you can soak the sliced red onion in cold water for 10-15 minutes, then drain thoroughly before adding.

3. Make the Creamy Tangy Dressing:
* In a separate medium-sized bowl, combine the mayonnaise, apple cider vinegar, sugar (or maple syrup/honey), Dijon mustard, celery seeds (if using), salt, and black pepper.
* Whisk thoroughly until the dressing is smooth, creamy, and well combined. Taste the dressing and adjust seasonings if necessary. You might prefer it a little sweeter, tangier, or saltier.

4. Combine and Chill:
* Pour the prepared dressing over the shredded cabbage and carrots in the large bowl.
* Using tongs or a large spoon, toss everything together until the vegetables are evenly coated with the dressing.
* For the best flavor, cover the bowl with plastic wrap and refrigerate the coleslaw for at least 30 minutes (ideally 1-2 hours) before serving. This allows the flavors to meld and the cabbage to soften slightly while still retaining its crunch.

5. Serve:
* Give the coleslaw a good stir before serving, as some dressing might settle at the bottom.
* Serve chilled.