Season chicken breasts all over with salt and pepper.

Place flour in a shallow dish and dredge chicken until lightly coated; shake off excess.

In a large skillet over medium-high heat, melt butter with olive oil.

Add the chicken and cook until golden brown on both sides, about 4 minutes per side. Remove chicken and set aside.

Add mushrooms to the skillet and sauté until tender, about 5 minutes.

Pour in the Marsala wine, scraping up any brown bits from the pan for extra flavor.

Stir in chicken broth and bring to a simmer. Cook until the sauce thickens, about 8 minutes.

Return chicken to the skillet and coat with the rich mushroom sauce. Simmer for 2 minutes more to heat through.

Garnish with fresh parsley and serve immediately over pasta or mashed potatoes.