Shred green and purple cabbage using a knife or grater.
Add shredded cabbage to a large mixing bowl.
Add grated carrots, sliced red onion, and chopped parsley.
In a small bowl, mix olive oil and apple cider vinegar.
Add lemon juice, honey, Dijon mustard, salt, and black pepper.
Whisk or shake the dressing until everything is well mixed.
Pour the dressing over the cabbage and vegetable mixture.
Toss the vegetables until evenly coated with the dressing.
Cover the bowl and chill in the fridge for 30 minutes.
Serve the cabbage slaw cold as a side or topping.