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To make the dressing, whisk all the ingredients together with 1 tbsp water and some seasoning, and set aside. Tip the lemon juice into a bowl. Use a swivel blade peeler to shave thin ribbons of celeriac into the lemon juice and toss to coat.
Thinly slice the celery sticks on an angle, but keep the leaves. Toss all the ingredients, except the Parmesan, with the celeriac and season with sea salt and a little pepper. Pile the salad onto 4 plates and top with the Parmesan shavings. Drizzle with the dressing and extra olive oil before serving.