Prepare the vegetable stock leaving the onion, carrot and celery to boil in 1 litre of water for about an hour. In the meantime, clean the artichokes and keep them in water with the juice of one lemon to avoid them becoming black, then cut them into thin strips, peel the stem and cut into rounds. Pour the oil and chopped onion into a saucepan and cook over a low heat until soft, add the artichokes, the salt and the pepper and the white wine. If needed add boiling water to finish cooking. Boil 8 dl of the stock in a separate saucepan, pour in the rice, stir and cover. Bring to the boil and cook the rice on a low heat. When the rice is three quarters cooked (after about ten minutes), add the artichokes, cover and finish cooking. Stir the rice with the cheese which has been finely chopped or cut into thin strips. Add some boiling stock, if necessary to keep the rice soft and serve.