1 3½-pound chicken, cut into 10 pieces
Kosher salt and freshly ground black pepper
2 tablespoons olive oil
1 medium onion, thinly sliced
1 cup thinly sliced white mushrooms
1 cup thinly sliced shiitake mushrooms
2 cloves garlic, thinly sliced
1 cup dry white wine
2 tablespoons Marsala wine
1 can (15 ounces) peeled plum tomatoes, coarsely chopped, with their juices
½ cup chicken broth
1 teaspoon minced fresh thyme leaves
¼ cup chopped fresh flat-leaf parsley
Pat the chicken dry and season to taste with salt and pepper. In a large skillet with a lid, heat the oil over medium-high heat. Add the chicken (in batches if necessary) and cook, turning, until browned, about 7 minutes. Transfer to a plate.
Add the onion to the pan and cook, stirring occasionally, for 3 minutes. Add the white and shiitake mushrooms and the garlic and cook, stirring until the mushrooms are softened, about 5 minutes.
Pour in the wine and Marsala and bring to a boil, scraping up any browned bits from the bottom of the pan. Add the tomatoes, broth, and thyme. Bring to a boil again and return the chicken to the pan along with its accumulated juices.
Reduce the heat and simmer, partially covered, turning the chicken pieces occasionally, for 40 to 45 minutes. The chicken should be very tender and the sauce should be slightly reduced and thickened. Season to taste with additional salt and pepper, if necessary. Garnish with parsley and serve.