In a small bowl, whisk together the Greek yogurt, orange juice, lemon juice, honey, orange zest, salt, and pepper until smooth. If using olive oil, slowly drizzle it in while whisking to emulsify. Set aside.
Julienne or thinly slice the apples and carrots. You can use a mandoline, a julienne peeler, or a sharp knife. Place them in a large mixing bowl. Add the chopped walnuts, parsley, and dried cranberries if using.
Pour the dressing over the salad and toss gently until everything is evenly coated. Transfer to a white serving plate. Garnish with extra parsley and a few whole walnuts. Serve immediately for maximum crunch.