Sprinkle the chicken with salt and pepper. Heat 1 tablespoon of the oil in a heavy large braising pan or nonstick skillet over medium-high heat. Add the chicken and cook until brown, about 1½ minutes per side. Transfer the chicken to a plate.

Add the shallots, onion, rosemary, and sage to the pan. Reduce the heat to medium-low and cook until the onion is almost tender, stirring frequently, about 5 minutes. Add the remaining tablespoon of oil to the pan, and then add the mushrooms. Sprinkle with salt and pepper. Sauté until the mushrooms begin to soften, about 5 minutes.

Add the broth and Marsala to the pan and bring to a boil, stirring up any browned bits. Return the chicken to the pan and bring the mixture to a boil. Cover the pan, reduce the heat to low and simmer 15 minutes. Turn the chicken over, cover the pan and continue cooking until the chicken is tender when pierce with a small, sharp knife, about 15 minutes longer.

Meanwhile, make the polenta.

Uncover the pan and boil until the sauce reduces slightly and flavors are concentrated, about 5 minutes.

Spoon a generous amount of the polenta into the center of 2 warmed plates. Spoon the chicken, vegetables, and sauce over. Sprinkle with additional thyme (see polenta recipe below) and serve.