Using a vegetable peeler, peel carrots into long ribbons. Alternatively, you can shred them in a food processor. Cover carrots with a wet paper towel to keep fresh.

To make the dressing, add shallot, white wine vinegar, Greek yogurt, Dijon mustard, and honey to a food processor. Pulse until combined. Drizzle in olive oil until emulsified. Add salt and pepper to taste.

To prepare salad, add the queso fresco, pistachios, and parsley. Toss with the shallot dressing, to taste. Start with half the dressing and add more as needed. Serve immediately. To make the recipe ahead, combine everything but the pistachios. Add the pistachios right before serving.