Place shredded cabbage, carrots, and cucumber slices in a large colander. Sprinkle with 1 teaspoon salt and toss. Let sit for 15 minutes, then rinse with cold water and squeeze dry with a clean kitchen towel.
In a small bowl, whisk together Greek yogurt, mayonnaise, apple cider vinegar, Dijon mustard, honey, and black pepper.
In a large bowl, combine the dried vegetables and fresh herbs. Pour dressing over and toss well.
Taste and adjust salt and pepper. Refrigerate for at least 30 minutes before serving for best flavor.