Set out a large salad bowl, and shred the purple cabbage into it using the side of a box grater with the largest holes or a sharp knife.
Next, finely dice the two apples into the bowl. Note that you can simply grate the apples into the bowl, but the result will be a softer, less crunchy slaw.
Now chop the herbs and add them to the bowl along with the raisins and cinnamon.
Mix the cabbage, apples, herbs, raisins, and cinnamon to incorporate. If you’d like to prepare this dish in advance, you can stop here and store the slaw overnight in the refrigerator covered.
Just before serving, drizzle the maple syrup and lime juice over the whole mixture, one at a time. Mix well to spread the liquids evenly throughout the slaw.