Put onto the heat a pan containing 6 1/4 cups of water, suitably salted, and when it is about to boil, drop in the yellow flour in a constant rain, while using the other hand to stir constantly with a wooden spoon to avoid lumps forming. Take care that the polenta, as well as being fairly dense, is well-cooked. If it is not pre-cooked, it takes half an hour minimum to cook. Dampen a work-surface with water and transfer the polenta to it spreading it out with the wet blade of a large knife, to a height of 1 inch or a little more. When the polenta is cold, cut into small rhombuses. Put into a casserole some cubes of ham and a little butter, with the onion, celery and carrot. Brown and add the tomato puree, douse with sufficient water, season with salt and pepper, and leave to cook gently. It is also possible to add some dried mushrooms, soaked in cold water and then chopped up, and some skinned sausage. Thoroughly butter an oven-dish. On the bottom arrange a layer of dumplings and dress with a little sauce and grated Parmesan. Make other layers in the same way. Finally pour on more sauce and Parmesan and scatter here and there some small pieces of butter. Put the oven-dish into a very hot oven for a quarter of an hour until the dumplings have formed a light crust that is golden and crunchy. Serve the dumplings on a plate with more tomato sauce.