Season the chicken breasts with salt and pepper, then dredge in flour, shaking off the excess.

In a large skillet, heat 2 tablespoons of olive oil and 2 tablespoons of butter over medium-high heat. Add the chicken and cook until golden brown on both sides, about 3-4 minutes per side. Remove chicken and set aside.

In the same skillet, add the remaining oil and butter. Add the sliced mushrooms and sauté until they are browned and their moisture has evaporated, about 5 minutes.

Pour in the Marsala wine and chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a boil and cook until the liquid is reduced by half, about 5 minutes.

Stir in the heavy cream and return the chicken to the skillet. Reduce heat to low and simmer until the chicken is cooked through and the sauce has thickened, about 5 minutes.

Serve the chicken and sauce hot, garnished with additional herbs if desired.