Core the cabbages and slice very finely. This can be done by hand or using a mandolin or a food processor attachment.
1/4 red cabbage, 1/4 white cabbage
Grate the carrots, apple, and onion. Use the large side of a box grater or the grating attachment in a food processor.
2 medium carrots, 1 large apple, cored, 1 small red onion
Place the vegetables into a large mixing bowl.
Pour the vinaigrette over the salad and use your hands to mix until well combined. Serve immediately or, if you have the time, allow it to rest for at least 30 minutes first.
Vegan coleslaw will keep for several days in a sealed container in the refrigerator. It can be eaten cold but is best served at room temperature.
Vinaigrette
Add the olive oil, vinegar, mustard, salt, and pepper to a small jar or bowl. Shake or whisk until well mixed and the vinaigrette is fully emulsified.