In a large saucepan, bring the stock to a boil. In a bowl, whisk the cornmeal and 1 cup cold water into a paste. Add the cornmeal to the boiling stock and cook over low, whisking occasionally, until thick and creamy, about 15 minutes. Season with salt, pepper and nutmeg to taste. Add the Taleggio; stir until the cheese melts. Cover to keep warm.
Meanwhile, in a small saucepan, simmer the porcini mushrooms in the stock and 1 cup water until the mushrooms are soft, about 5 minutes.
In a large, deep skillet, heat the oil, two turns of the pan, over medium. Season the chicken liberally; cook until browned, 3 to 4 minutes per side. Transfer to a plate. Add the butter to the skillet. When the butter foams, add the cremini mushrooms. Season and cook, stirring occasionally, until the mushrooms are browned, about 4 minutes. Add the shallots, celery, garlic, rosemary and thyme; stir until the shallots soften, 2 to 3 minutes . Add the tomato paste and stir until fragrant, 1 to 2 minutes. Add the wine and simmer until reduced by half, 3 to 4 minutes. Using a slotted spoon, add the porcini to the skillet, then add the mushroom cooking liquid, leaving any sediment behind. Slide the chicken back into the skillet and simmer until cooked through, 8 to 10 minutes. Add the parsley. Pour the polenta onto a serving platter; top with the chicken and mushrooms.