Season chicken with salt and pepper. Dredge in flour and shake off excess.
Heat 2 tablespoon olive oil in large skillet over medium-high heat. Sear chicken 5–6 minutes per side until golden and cooked through. Remove and set aside.
Lower heat to medium, add remaining 2 tablespoon olive oil, and sauté mushrooms until golden brown, about 4–5 minutes.
Deglaze with Marsala wine, scraping up browned bits. Simmer until reduced by half.
Add chicken broth and simmer again until reduced by half.
Lower heat to low. Stir in 2 tablespoon butter until emulsified.
Return chicken to the skillet and simmer for 5 more minutes to absorb flavor.
Season with salt and pepper to taste, garnish with chopped parsley, and serve.