In a medium bowl, whisk together all the ingredients for your dressing. Taste test and adjust if desired.
In a large bowl combine your shredded green cabbage, purple cabbage, and Brussels sprouts.
Quickly chop your apple then immediately toss it with the fresh lemon juice, then add it to the bowl with the cabbage.
Drizzle the dressing over everything then toss well to coat.
Your coleslaw stays good in the fridge for 2 days, best enjoyed within 24 hours.