Melt the remaining tablespoon of butter in the pan. Add the mushrooms and cook, stirring frequently, until the mushrooms begin to brown, 3 to 4 minutes. Add the shallots, garlic, and 1/4 teaspoon of salt; cook for 1 to 2 minutes more. Add the broth, Marsala, heavy cream, thyme, 1/4 teaspoon salt, and 1/8 teaspoon of pepper; use a wooden spoon to scrape and stir. Bring the liquid to a boil, then reduce the heat to medium and gently boil, uncovered, until the sauce is reduced by about half, slightly thickened, and darkened in color, 10 to 15 minutes. Add the chicken back to the pan, along with any juices that accumulated on the plate. Reduce the heat to low and simmer until the chicken is warmed through and the sauce thickens a bit more, 2 to 3 minutes. Sprinkle with parsley and serve.