Place 5 cups water in a 4-quart saucepan and bring to a boil. Add a tablespoon of salt. Drizzle in polenta in a thin stream into the pot, whisking constantly, until all polenta is incorporated and mixture begins to thicken. Switch to a wooden spoon, pull off heat and continue to stir until thick as paste. Add stracchino, stir through and set off heat. Set aside.
Meanwhile, in a 12- to 14-inch sauté pan, heat the olive oil over high heat until smoking. Add the onion and cook until light golden brown, about 5 minutes. Add the mushrooms and cook until they have given off most of their water and it has evaporated, 8 to 10 minutes. Add the wine, tomato sauce, butter, and salt and pepper to taste, reduce the heat to medium, and cook until the consistency of a thick sauce, about 5 more minutes.
Divide polenta among 4 bowls, top each with mushroom ragu and serve immediately.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, 8 to 10 minutes. Add the thyme and carrots and cook 5 minutes more, until carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.