Prepare the vegetables: Grate the carrot into a medium bowl using the large side of a grater or a mandolin. Add the cucumber and red onion, if using. Stir in the chopped parsley.

Make the dressing: In a separate small bowl, whisk together olive oil, apple cider vinegar, garlic (if using), mustard, honey, salt, and black pepper until emulsified.

Combine: Pour the dressing over the carrot mixture. Toss well to combine and coat the vegetables evenly.

Taste and serve: Adjust salt and pepper if needed. Serve immediately or refrigerate until ready to eat.