Brush the mushroom caps gently with a clean cloth to wipe away any dirt. Arrange them, underside up, on a sheet pan, drizzle with the olive oil and balsamic vinegar, then sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper. Bake for 20 minutes, until tender. Set aside. Lower the oven to 375 degrees.
Meanwhile, make the polenta. Pour the stock and half-and-half into a large saucepan and bring it to a boil. Lower the heat and, while whisking constantly, slowly sprinkle the cornmeal into the boiling liquid. Simmer for 6 to 8 minutes, stirring almost constantly with a wooden spoon, until the polenta is thick and smooth. Off the heat, stir in the mascarpone, 1 teaspoon salt, and 1/2 teaspoon pepper. Pour into an 8 x 11 x 2-inch baking dish.
Arrange the mushrooms, underside up, in one layer over the polenta. Sprinkle on the Gorgonzola and bake for 25 to 30 minutes, until the polenta is bubbly and the cheese is melted. Sprinkle with salt and serve hot.
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This recipe has been updated and may differ from what was originally published or broadcast.