Preheat the oven to 200°C/fan 180°C/gas mark 6. Using a swivel peeler or mandolin, peel all the vegetables thinly, discarding the outer peel. Spread out the beetroot on a kitchen paper-lined baking tray and the parsnip and carrot on a separate, larger, kitchen paper-lined baking tray, and leave for 30 minutes to soak up any excess moisture.
Drizzle 3 tsp oil over the carrots and parsnips and 2 tsp oil over the beetroot and, using your hands, toss them so they're evenly coated and are in a single layer. Remove the kitchen paper.
Season lightly with black pepper and roast on the middle shelves 10-12 minutes for the beetroot and 15-16 minutes for the carrots and parsnips, until they look crispy and shrunken, and the carrots and parsnips are light brown. Once done, leave to cool slightly on kitchen paper before serving.