For dressing, in a bowl, whisk together orange peel, orange juice, lemon juice, vinegar, oil (if you like), sugar, honey, and salt. Set aside.
In a large bowl, combine the carrots, apples, and parsley. Pour dressing over all. Toss to coat. Cover and chill for at least 1 hour or up to 24 hours. Makes 8 side-dish servings.