DRESSING: In a medium-sized bowl, mix together all of the dressing ingredients. Taste and adjust to personal preference. If desired, add in the lemon juice (add slowly, to personal preference). Refrigerate while preparing the cabbage.
CABBAGE, CARROTS, AND APPLE: Start by removing any outer leaves that are browned or crumpled. Cut the green cabbage exactly in half and then in half again (to get 4 quarters). Cut out the core of each quarter. Slice each cabbage quarter into very thin shreds. To make things faster, use a mandoline slicer here. If the shreds are long, cut in half. Transfer the sliced cabbage to a salad spinner base. Wash thoroughly and spin to dry completely. Repeat with red cabbage. Shred carrots on the small side of a cheese grater. Cut apple into thin slices. Cut the slices into matchsticks. Add the green cabbage, red cabbage, carrots, and apple to a very large bowl.
COMBINE: Pour the dressing over everything, and toss well to combine. It will seem dry at first, but keep mixing. Cover and refrigerate, for at least 20-30 minutes and preferably 2 hours or up to overnight.
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Notes
Note 1: Chilling time: This recipe benefits from spending some time in the fridge. I recommend 2 hours at a minimum, and up to a day in advance. Not only does everything become more flavorful, it also helps soften the cabbage. Be sure to toss well again before serving.