Wash and peel the celery root and apple. Grate the celery root and julienne the apple into thin strips.
Toss the celery root and apple with lemon juice to prevent browning, then combine them in a large bowl.
In a separate small bowl, whisk together the Greek yogurt (or vegan alternative), mustard, honey (or agave syrup), salt, and pepper until smooth.
Pour the yogurt dressing over the celery root and apple mixture, and gently fold to coat everything evenly.
Toast the walnuts in a dry skillet over medium heat until lightly golden brown, then let them cool slightly.
Sprinkle the salad with the toasted walnuts and fresh parsley. Serve immediately, or refrigerate to allow the flavors to meld.
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