Combine the green cabbage, purple cabbage, and carrots in a mixing bowl.
Separately, whisk together the olive oil, basil, parsley, apple cider vinegar, honey, salt, and pepper in a small mixing bowl.
Pour the herb dressing over the cabbage and carrots and stir to combine.
This coleslaw can be made 1 day in advance and refrigerated until ready to serve. If you like your coleslaw with some crunch, make it no more than 30 minutes before serving.