Cook the potato and parsnip in separate, large saucepans in salted, boiling water until tender; the potatoes will take 10-15 minutes, the parsnips will take a little longer. Drain them when they are ready and let them cool a little.
After cooling, combine the parsnips and potatoes in a large mixing bowl. Add the oil, sugar, Chinese five-spice and seasoning and toss lightly to coat. Heat together the butter in a large saucepan set over a moderate heat until it stops foaming.
Add the cinnamon sticks and star anise, then follow with the potatoes and parsnips and pan-fry for 2-3 minutes, moving them around the pan every now and then. Reduce the heat a little once the vegetables have taken on some colour and cook for a further 2-3 minutes.
Remove from the heat and spoon into serving bowls. Serve immediately.