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1
Bring water to a simmer in a 3- to 4-quart heavy saucepan. Add grits in a slow stream, whisking until incorporated. Simmer, stirring occasionally with a long-handled whisk or wooden spoon, until liquid is absorbed and polenta is thick and soft, about 30 minutes. (Grits will have a loose, risotto-like consistency.) Remove from heat and stir in cream, cheese, salt, and pepper. Keep warm, covered.
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2
If using porcini, halve if large, then slice lengthwise into 1/4-inch-thick slices. If using oysters, trim spongy base if necessary and slice caps into 1/2-inch-wide strips. If using chanterelles, leave small mushrooms whole, halve if medium, and quarter if large. If using lobsters, cut into 1/2-inch pieces. If using hedgehogs, trim base of stems and halve caps if large.
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3
Heat oil in a 10-inch heavy skillet over moderately high heat until hot but not smoking, then saute mushrooms, garlic, salt, and pepper, stirring occasionally, until mushrooms are golden and any liquid they give off is evaporated, 6 to 8 minutes.
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4
Add water, butter, lemon juice, and parsley and heat, swirling skillet, until butter melts and liquid forms a sauce.
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5
Top each serving of polenta with mushrooms and mascarpone. Serve immediately (polenta stiffens as it cools), sprinkled with Parmigiano-Reggiano.
