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1
Prepare the polenta. In a medium pot or saucepan, bring the broth, water and salt to a boil. Whisk in the polenta. When the water starts boiling again, reduce the heat to low and keep on stirring for about 10 to 15 minutes, until the polenta bubbles assume a rhythm of their own. At this point, you can let the polenta bubble without heavy supervision, for about 45 minutes. Pay a visit to the pot to stir from time to time (a bit more often towards the end of cooking). Remove the polenta from the stove, add the butter and mix well.
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2
Make the sauce. Cut the mushroom caps into 1/4-inch cubes. If you are using stems (I do, except for very hard parts), make sure that you cut them into really small pieces, as they are tougher than the caps.
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3
In a medium saucepan, heat about a tablespoon of sunflower oil over medium heat. Add in the shiitakes and cook for about 3 minutes, until browned and soft. Remove the shiitakes from the pan, and keep them in a medium-sized bowl.
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4
In the same pan, heat a tablespoon of butter, add the apples, and cook over moderately high heat until browned, for about 3 minutes. Make sure not to overcook the apples. Add the apples to the mushrooms.
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5
Deglaze the pan with Calvados and pour the sauce over the apples and mushrooms.
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6
In a separate pan, heat a tablespoon of sunflower oil, add the shallots, and cook for about 2 to 3 minutes, until soft. Add the garlic and cook for another minute, until fragrant. Add the apple and mushroom mixture, sage, and marjoram. Sprinkle with about a tablespoon of flour, mix well, and pour in the broth. Simmer for a couple of minutes over medium heat, until the sauce thickens (if needed you can always add another pinch of flour, or if the sauce is too thick a bit more broth). Add in the heavy cream, and simmer for another minute or two. Remove from the heat and season with salt and pepper.
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7
Pour the polenta onto individual plates. Spoon the sauce on top and garnish with herbs. Serve warm.
