1. In a medium saucepan, bring the water and 1 teaspoon salt to a boil. Add the cornmeal in a slow stream, whisking constantly. Whisk in 3 tablespoons of the oil. Reduce the heat and simmer, stirring frequently with a wooden spoon,until the polenta is thick, about 20 minutes. Stir in the Parmesan. Remove from the heat but cover to keep warm.
2. Meanwhile, in a medium bowl, mix together the ricotta, mascarpone, and 1/8 teaspoon salt. Put in the refrigerator.
3. In a large frying pan, heat the remaining 2 tablespoons oil with the butter over moderately high heat. Add the mushrooms, garlic, and 1/4teaspoon salt. Cook, stirring, until the mushrooms are golden, 5 to 10 minutes. Stir in the parsley and pepper.
4. Stir the polenta. It should be thick but still pourable. If it's too thick, stir in more water. You may need as much as a cup. Using a large spoon or a medium ice-cream scoop, put three mounds of the cheese mixture onto each of four plates. Ladle the hot polenta over the mounds of cheese and top with the mushrooms.
Wine Recommendation: The tannins in a red wine will be tamed by the richness of the cheese in this dish, pushing the wine's flavor to the fore. A Rosso di Montalcino, Brunello's fruitier cousin, will demonstrate this delectably.