Place the chicken breasts between two sheets of plastic wrap and pound to 1/2-inch thickness.
Season both sides of the chicken with salt and black pepper, then dredge in flour, shaking off excess.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Sear the chicken for 3-4 minutes per side until golden brown, then remove from the pan.
Add the remaining butter and sauté mushrooms until browned and tender, about 5 minutes.
Pour in the Marsala wine and chicken broth, scraping up any browned bits from the pan.
Simmer for 3-5 minutes, then stir in heavy cream (if using).
Return the chicken to the pan and let simmer for another 5 minutes until heated through.
Garnish with fresh parsley and serve hot.