Thinly slice the celery sticks and chop the celery leaves roughly. Thinly slice the red apple.
In a bowl, whisk together the white wine vinegar, mustard, honey (or sugar), salt & pepper. Gradually pour in the olive oil while continuously whisking.
In a separate large bowl, toss together the celery and celery leaves with the apple, dressing, and Parmesan. Serve immediately or refrigerate until serving. This tastes best the day of making, but you can refrigerate leftovers for a few days (refresh them with a little vinegar or salt if necessary).