Shred the cabbage either by slicing thinly with a knife or by using the slicing attachment on a food processor. Peel the carrots if necessary and shred.
Remove the cilantro leaves from their stems and chop or tear the leaves into small pieces. Combine vegetables in a large bowl.
In a medium bowl, mix the dressing ingredients together with a whisk. Taste, and add a little more vinegar if you would like. Pour the dressing over the vegetables and mix to combine.
Serve immediately or refrigerate for an hour or two first.