How to Make It
In a large, deep skillet, melt 1 tablespoon of the butter in 1 tablespoon of the olive oil. Add half of the shallots and garlic and all of the chanterelles and oyster mushrooms and cook over moderately high heat, stirring occasionally, until softened and golden, about 6 minutes. Scrape the mushrooms onto a plate.
In the same skillet, melt the remaining 1 tablespoon of butter in the remaining 1 tablespoon of olive oil. Add the remaining shallots and garlic along with the shiitake mushrooms and cook over moderately high heat, stirring occasionally until softened and golden, about 6 minutes. Return all of the mushrooms to the skillet, season with salt and pepper and cook for 1 minute. Add the rich chicken stock and thyme sprigs to the skillet and simmer for 5 minutes. Discard the thyme sprigs.
In a large saucepan, combine the milk, stock and butter and bring to a boil. Whisk in the polenta and cook over moderate heat, stirring constantly with a wooden spoon until thick, about 8 minutes. Remove from the heat and stir in the heavy cream, mascarpone, herbs and Parmesan. Season with salt and pepper.
Spoon the polenta onto plates, top with the mushroom ragout and serve right away, passing more grated Parmesan at the table.
Rich chicken stock is sold in the freezer section of many supermarkets.