Prepare the sauce: In a large, heavy-bottomed pot or Dutch oven, heat the oil over medium heat. Add the onion, celery, and carrot cut into large chunks and sauté until lightly browned.
Remove the vegetables from the pot and set them aside. Add the sausages and pork spareribs to the pot, browning them well on all sides.
Pour in the tomato purée and return the sautéed vegetables to the pot. Reduce the heat to very low, cover, and let simmer gently for about 2 hours.
Once the sauce has thickened and the meat is tender, stir in a tablespoon of chopped fresh parsley and hot chili pepper to taste. Season with salt.
Prepare the polenta: In a copper pot or large heavy saucepan, bring 2 liters of water to a boil. Add salt, then gradually pour in the cornmeal in a steady, thin stream, whisking constantly to prevent lumps from forming.
Reduce the heat to low and cook for approximately 50 minutes, stirring continuously.
Assemble and serve: When the polenta is ready, pour and spread it out across a large wooden board (tagliere). Ladle the rich sauce and meats evenly over the top. Serve family-style in the traditional way, with diners seated around the board, and offer the grated Pecorino cheese on the side.