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Heat oven to 200C/180C fan/gas 6. Put the parsnips on a baking tray, drizzle with the olive oil, season well and roast for 30 mins or until tender and nicely caramelised. Reduce the temperature to 180C/160C fan/gas 4.
In a large bowl, whisk together the cream, eggs, half the butter, half the cheese and half the thyme. Season well, then add the truffle oil, brioche and parsnips, and leave for 10 mins.
Lightly oil a medium baking dish and tip in the soaked brioche mixture. Heat the remaining butter in a shallow pan and cook until the butter turns brown. Add the hazelnuts and remaining thyme and cook for 2 mins before spooning over the top of the pudding. Cover the dish with foil, and cook in the oven for around 50 mins until puffed up and starting to caramelise. Remove the foil, sprinkle with the remaining cheese and place back in the oven for 15 mins to brown fully. Scatter over the black truffle, if using, add an extra drizzle of truffle oil, the extra thyme and serve.