Combine the cabbage, carrots, apple, salt, and lime juice in a large bowl.
In a medium skillet, cook the minced onion in 1 tablespoon of olive oil for 5 minutes. Add the ginger and cook for an additional 30 seconds.
In a jar, mix the remaining tablespoon of olive oil with the honey and rice vinegar. Add the veggies from pan.
Pour the dressing over the cabbage mixture and mix well. Refrigerate for an hour before serving. This will wilt a bit if you leave it in the refrigerator for a few days, but it still tastes great.