Melt the remaining tablespoon of butter in thepan. Add the mushrooms and cook until the mushrooms begin to brown, 3 to 4minutes, while stirring frequently so they do not burn or stick. Add theshallots, garlic, and a pinch of salt; cook for 1 to 2 minutes more. Add thebroth, Marsala, heavy cream, thyme and 1/8 teaspoon of red pepper. With awooden spoon, scrape any brown bits from the pan into the liquid. Bring theliquid to a boil, then reduce the heat to medium and gently boil, uncovered,until the sauce becomes thicker and darkened, and is reduced by about half,about 10 to 15 minutes. The goal is a thin cream sauce which will start to gettoward the desired consistency toward the very end of the cooking time. Add thechicken and any juices that may have accumulated with it, back to the pan. Reducethe heat to simmer until the chicken is warmed through and the sauce thickens abit more, 2 to 3 minutes. Sprinkle with parsley and serve.