Slice the white and red cabbage thinly. Use a mandoline if you have one. Grate the carrots or use a julienne vegetable peeler to cut them into long thin strips. Chop up the cilantro leaves if using. Combine all ingredients in a large bowl.
Mix the mayonnaise, white wine vinegar and Dijon mustard in a small bowl. Add the dressing to the slaw and toss to combine. Season with salt and pepper to taste.