Preheat the oven to 200˚C, gas mark 6. Cut large pieces of the Jersualem artichokes into quarters, leaving thin ends whole, then thinly slice so all are roughly the same size. Put in a roasting tin with 2 tbsp oil and season. Cover with foil and roast for 35 minutes, then uncover and roast for 10-15 minutes until tender and golden.
Meanwhile, heat the remaining 1 tbsp oil and 50g butter in a heavy-based pan over a low heat. Add the onion, carrot and garlic and cook, stirring occasionally, for 10 minutes until soft but not coloured. In a separate pan, bring the stock to a simmer. Add the rice to the softened vegetables and stir until coated in the butter and oil. Cook for a few minutes, then pour in the wine. Stir for 1-2 minutes until the wine has evaporated.
Add the stock one ladleful at a time, waiting for the liquid to be absorbed before adding the next ladle, keeping the lid on between additions to create steam. Continue until all the stock has been added and the rice is cooked through, with a little bite remaining (about 40 minutes). Take the pan off the heat and stir in 25g grated cheese and the remaining 25g butter. Cover and stand for 5 minutes. Stir through of the artichokes. Serve the risotto with the remaining Jerusalem artichokes on top, and the basil leaves and remaining cheese scattered over.
