Season the chicken breasts with salt and pepper and dredge them in the flour.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Cook the chicken breasts for about 5 minutes on each side until they're golden brown and cooked through. Remove from the pan and set aside.
In the same skillet, add the remaining tablespoon of butter and sliced mushrooms. Cook until the mushrooms are browned and tender.
Pour the Marsala wine into the skillet to deglaze the pan, stirring to scrape up any browned bits from the bottom.
Add the chicken broth and bring the mixture to a simmer. Cook until the sauce is slightly thickened.
Return the chicken breasts to the skillet and spoon the sauce over them. Allow to simmer for another 5 minutes.
Garnish with chopped parsley before serving. Serve with pasta or mashed potatoes.