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PREHEAT THE OVEN to 200F.
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TO MAKE THE OVEN-ROASTED TOMATOES: Brush a large baking sheet with olive oil and lay the tomatoes on it in a single layer, cut side up.
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Sprinkle them with salt and pepper, then turn cut side down.
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Brush the tops of the tomatoes with olive oil and sprinkle with salt and pepper.
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Roast for 4 to 6 hours, regulating the heat so that it doesnt get so hot that the tomatoes burn.
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Since the tomatoes must cook at a very low and constant temperature, it is best to use an oven thermometer.
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Prop the oven open by 1 inch with a dish towel if the temperature is difficult to regulate at such a low heat.
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The tomatoes are done when they are shrunken, dehydrated, and shriveled on top but still quite juicy underneath.
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Cool on the baking sheet and wrap with plastic wrap until needed.
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TO MAKE THE SAUCE: Rinse and drain the Swiss chard.
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Remove the leaves from the ribs, trim and discard the woody bottoms, and slice the ribs 3/8 inch thick.
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Coarsely chop the leaves and set both aside separately.
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IN A LARGE HEAVY SAUTE PAN, cook all the sausages over medium-low heat for about 15 minutes, stirring occasionally, or until no trace of pink remains.
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With a slotted spoon, remove the sausage to a bowl, then pour off and discard the fat from the pan.
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Wipe the pan with a paper towel.
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Over medium heat, combine the olive oil, onion, and carrot and saute for 6 to 8 minutes, or until the onion is translucent.
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Return the sausage to the pan, add the sage and garlic, and stir for 2 minutes.
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Add half the wine and half the tomato paste and stir until most of the wine has evaporated.
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Cut the oven-roasted tomatoes in half lengthwise and then again crosswise.
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Add them to the pan.
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Add the remaining wine, remaining tomato paste, and the ribs of the Swiss chard.
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Cover the pan and cook, stirring occasionally, for 10 minutes.
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Remove from the heat, cover, and set aside while you cook the polenta.
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SOAK THE PORCINI MUSHROOMS in 1 cup of very hot water for 30 minutes, squeeze dry and finely chop them.
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Strain the soaking water.
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Set aside both mushrooms and soaking water.
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TO MAKE THE POLENTA: In a large heavy saucepan, heat the olive oil over medium heat.
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Add the onion and garlic and saute, stirring occasionally, for 5 to 6 minutes, or until softened.
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Add the porcini to the pan and stir for 1 minute more.
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30
Add the chicken stock, the mushroom-soaking liquid, and salt and increase the heat to high.
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When the liquid is simmering, gradually sprinkle the polenta over in a very slow, thin stream, whisking constantly in the same direction until all the grains are incorporated and no lumps remain.
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Reduce the heat to very low.
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Switch to a wooden paddle and stir every 1 or 2 minutes for 25 to 30 minutes, or until the mixture pulls away from the sides of the pan and the grains of polenta have softened.
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Stir in the butter, pepper to taste, and Parmesan and remove from the heat.
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35
RETURN THE SAUCE TO MEDIUM-HIGH HEAT, add the Swiss chard leaves and cover.
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After 2 minutes, remove the lid and stir to mix.
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Repeat twice more and, after about 6 minutes when the chard leaves are tender, remove from the heat.
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38
Mound some of the soft polenta onto each of 6 heated dinner plates, make a well in the center and spoon the sauce over.
