Prepare the dressing: add all of the vinaigrette ingredients to a small mixing bowl and whisk to combine. Alternatively, you can make the dressing in a blender cup or shake it in a capped mason jar. Set aside.
1/4 cup lime juice, 1/4 cup extra virgin olive oil, 1 1/2 tablespoons honey, 1/4 teaspoon sea salt, 1/4 teaspoon ground black pepper, 1 tablespoon mayo
Thinly slice or shred the green cabbage, purple cabbage, and carrots and add to a large serving bowl. You can do this with a sharp knife, a grater, or a food processor.
1/2 small head green cabbage, 1/2 small head purple cabbage, 2 whole carrots
Chop the cilantro and add to the bowl of veggies. (I like to chop the leaves and most of the stems, but leave the tougher bottom half of the stems out of the salad).
1 bunch cilantro
De-seed and dice the jalapeño. Slice the green onions. Add these items to the slaw.
1 jalapeño, 4 green onions
Pour the dressing over the slaw and toss to coat. Can serve immediately, or be made ahead of time. Serve same day for best taste and texture.