Spray a miniature loaf pan (5 3/4 by 3 1/4 by 2-inches) with nonstick vegetable spray. In a medium saucepan bring 2 cups salted water to a boil. Whisking constantly, add polenta in a slow steady stream. Reduce heat to medium and continue to cook, whisking constantly for 3 minutes. Stir in grated Parmesan, salt, pepper and butter. Pour polenta into prepared pan. Transfer to refrigerator until completely cool, about 2 hours. You can also serve the mushrooms over soft polenta, if desired.
In a large skillet, heat 2 tablespoons oil over high heat. Add mushrooms and cook, stirring occasionally, until golden brown, about 10 minutes. Stir in parsley and thyme. Add Madeira and cook, stirring to scrape up browned bits from the bottom of the pan, until liquid is almost evaporated, about 2 minutes. Taste and adjust for seasoning.
While mushrooms are cooking, remove polenta from refrigerator. Using a small spatula, loosen polenta and remove from pan. Turn out onto cutting board and cut into 1/2-inch slices. Heat remaining 2 tablespoons oil in a large nonstick skillet over medium-high heat. Add polenta slices and cook until golden brown, about 4 minutes per side, add additional oil as needed to avoid sticking. Serve topped with sauteed mushrooms and garnished with Parmesan curls. Serve immediately.
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