Shred carrots using the shredding disk on a food processor (or a box grater). Pour carrots into a large bowl, and swap the shredding disk for the standard processor blade.

Add oil, vinegar, mustard, honey, and parsley to the processor and pulse until parsley is chopped and mixture is blended. Add salt and pepper to taste.

Pour dressing over carrots (you might not need all of it) and toss to coat. Serve immediately or cover and chill until ready to serve.