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1
Heat the oven to 350.
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2
In a medium saucepan, bring the water and 1 teaspoon of the salt to a boil.
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3
Add the cornmeal in a slow stream, whisking.
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4
Whisk in 1 tablespoon of the oil and 1/4 teaspoon of the sage.
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5
Reduce the heat and simmer, stirring frequently with a wooden spoon, until very thick, about 20 minutes.
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6
Stir in 3 tablespoons of the Parmesan.
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7
Meanwhile, butter an 8-by-12-inch baking dish.
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8
In a large frying pan, melt 1 tablespoon of the butter with 1 tablespoon of the oil over moderately high heat.
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9
Add half the mushrooms, 1/4 teaspoon each of the salt and sage, and 1/8 teaspoon of the pepper.
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10
Cook, stirring frequently, until the mushrooms are golden, about 5 minutes.
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11
Remove.
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12
Repeat with the remaining mushrooms, 1 tablespoon each butter and oil, 1/4 teaspoon each salt and sage, and 1/8 teaspoon pepper.
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13
Pour half the polenta into the baking dish and spread in an even layer.
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14
Top with half the mushrooms, followed by half of the fontina and 2 tablespoons of the Parmesan.
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15
Repeat with the remaining polenta, mushrooms, fontina, and Parmesan.
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16
Bake until the cheese is bubbling, about 15 minutes.
