Prepare the chicken: Place a chicken breast between plastic wrap or parchment and gently pound to about 1 cm (½-inch) thickness. Repeat with the remaining chicken breasts.

Season and dredge: Combine the flour, salt, and pepper on a plate. Dredge each chicken breast in the flour mixture, shaking off the excess.

Brown the chicken: Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook the chicken breasts for 4-5 minutes per side, until golden and almost cooked through. Transfer chicken to a plate and set aside.

Sauté mushrooms: Add the remaining 2 tablespoons olive oil to the same skillet. Add sliced mushrooms and cook for 5-7 minutes until browned and their liquid has evaporated.

Deglaze: Pour in the Marsala wine, scraping up any browned bits from the pan. Let it simmer for 2 minutes to reduce slightly.

Make the sauce: Add chicken broth and let the sauce simmer for another 3–4 minutes.

Finish chicken: Return the chicken breasts to the pan and simmer for 5 minutes, spooning sauce over the top, until the chicken is cooked through and the sauce thickens.

Serve: Sprinkle with chopped parsley and serve hot.