Bring water, 1 tablespoon of butter, and 1/2 teaspoon of salt to the boil in a heavy sized pot. Gradually beat in the polenta. Reduce heat to medium-low. Stir continuously until polenta thickens, about 5 minutes. Pour the polenta into a 9-by 9-inch greased frying pan, extending it to 1/3-inch thick. Cover and let stand at room temperature until snug, about 15 minutes. Meanwhile, heat the oil in a large, heavy skillet on medium-high heat. Add mushrooms and onions. Sprinkle with 1/2 teaspoons of salt and 1/4 teaspoons of pepper and bake until juices are evaporated, about 8 minutes. Add the garlic and bake until the mushrooms are golden, about 2 minutes more. Reduce heat to medium-low. Add the Marsala. Cover and simmer until Marsala is reduced by about half, about 5 minutes. Stir in the flour and the remaining 2 tablespoons of butter in a small bowl to form a paste, then stir the pasta into the mushroom mixture. Cover and let simmer until the sauce is slightly thickened, about 2 minutes. Remove it from the fire. Stir the parsley in the hash. Season the hash, to taste, with more salt and pepper. Cut the polenta into 36 square-sized bite. Arrange the polenta squares on a tray. Spoon the hot hash on top of the polenta and serve immediately.