Cook the polenta: In a medium, heavy pot over high heat bring the cream, stock, salt, and nutmeg to a boil. Add the polenta gradually, whisking constantly. When the mixture thickens, switch to a wooden spoon and adjust the heat to maintain a bare simmer. Cook, stirring often, until thick, smooth, and creamy, about 15 minutes. Add the Parmesan and stir. Keep the polenta warm over low heat, stirring occasionally. If the polenta gets dry as it sits, stir in about 1/4 cup of warm stock or cream.
Saute the mushrooms: In a medium skillet over high heat, heat the olive oil. When the oil is hot, sprinkle in the mushrooms in a single layer. Don't stir them! Let them sizzle until they have caramelized on the bottom, about 2 minutes. When the bottoms are caramelized, toss them once and season with salt and pepper, to taste. Continue to cook without stirring for about 5 minutes. Season mushrooms with salt and pepper. Add the butter and cook until it begins to brown, then add the garlic. Continue to cook until the garlic begins to brown. Add the thyme and cook for about 10 seconds. Add the lemon juice and cook until the liquid evaporates. Add the wine, and simmer until the mushrooms are glazed with the sauce. Add the parsley. Then stir and remove the pan from the heat.
Place or pipe about 1 tablespoon of warm polenta onto a spoon. Place about 1/2 teaspoon of the mushroom on top of the polenta. Garnish with grated Parmesan. Serve immediately.