How to Make It
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.
Meanwhile, in a medium bowl, mix together the ricotta, mascarpone, and 1/8 teaspoon salt. Put in the refrigerator.
In a large frying pan, heat the remaining 2 tablespoons oil with the butter over moderately high heat. Add the mushrooms, garlic, and 1/4 teaspoon salt. Cook, stirring, until the mushrooms are golden, 5 to 10 minutes. Stir in the parsley and pepper.
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.