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Heat the oil in a large frying pan, add the carrot, swede and onions, and cook for 8 mins. Add the garlic, rosemary, tomato purée and yeast extract, and cook for a further 5 mins. Add the tomatoes and white wine and scrape all the goodness off the bottom of the pan. Pour in the stock, add the mushrooms and chestnuts, then simmer for 8 mins until the sauce is reduced and thickened. Remove from the heat and allow to cool slightly.
Meanwhile, to make the topping, put all the vegetables in a large pan of salted water and bring to the boil. Cook for 12 mins or until the vegetables are tender. Drain, then allow to steam-dry for 5 mins. Roughly mash the roots with the butter, milk and some seasoning.
Heat oven to 190C/170C fan/gas 5. Pile the mushroom mixture into an ovenproof dish, top with the mash, then cook for 30 mins until golden and bubbling. Serve with some buttered greens, if you like.