Quarter the cabbage through the core, and then cut out the core. Cut each quarter crosswise in half and finely shred
Place the shredded cabbage in a very large bowl (you will have a 6 to 8 cups)
Add the shredded carrot and parsley to the cabbage and toss to mix
In a separate bowl, stir the mayonnaise, vinegar, mustard, celery seeds, salt, and pepper together. Taste for acidity and seasoning then adjust as desired
Pour two-thirds of the dressing over the cabbage and carrot then mix well. (Clean hands are the quickest tool). *If the coleslaw seems dry, add a little more of the dressing
Eat right away or let it sit in the refrigerator for about an hour to let the flavors mingle and the cabbage to soften