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1
In a large saute pan or frying pan over medium heat, melt 1/4 cup of the butter. When bubbly, add the mushrooms, raise the heat to medium high, and saute, tossing often, until tender, about 5 minutes. Do not let brown. Season with salt and a little nutmeg and remove from the heat. Cover to keep warm.
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2
Position a rack in the center of an oven and preheat to 425 degrees F . Butter a 2 1/2-qt. baking dish.
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3
In a deep, heavy saucepan over high heat, bring the water to a rapid boil. Add 2 tsp salt and, while stirring continuously with a long-handled spoon, gradually add the polenta in a thin, steady stream until all has been incorporated. Continuing to stir constantly to keep lumps from forming, reduce the heat until the mixture only bubbles occasionally. Continue to cook, stirring, until smooth and creamy, about 20 minutes; be careful to scrape the bottom and sides of the pan to avoid sticking or lumping. Remove from the heat. Cut the remaining 1/4 cup butter into small cubes and add to the polenta, a few cubes at a time, stirring until melted after each addition. The polenta should be soft and spreadable.
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4
Spread one-third of the polenta over the bottom of the prepared baking dish. Spread half of the mushrooms in a layer on top, and then cover with a layer of half of the cheese slices. Repeat with half of the remaining polenta, than all of the remaining mushrooms and cheese. Top with the remaining polenta.
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5
Place in the oven and bake until lightly browned, about 20 minutes.
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6
Cut into squares and serve immediately.
