Prep the Chicken: Season the chicken breasts with salt and pepper on both sides. Place the flour on a plate or shallow dish and coat the chicken evenly, shaking off any excess.
Sear the Chicken: Heat 2 tablespoons of butter and 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the chicken breasts and for about 4 minutes cook both sides until golden brown. Take out the chicken into a plate and set aside.
Sauté the Mushrooms: In the same skillet, add the remaining 2 tablespoons of butter and 2 tablespoons of olive oil. Add the sliced mushrooms and sauté until they are golden brown and have released their juices, about 5-6 minutes. Now add minced garlic, stir, and cook for an additional minute.
Create the Marsala Sauce: Pour the Marsala wine into the skillet and bring it to a simmer, scraping the bottom of the pan to loosen any browned bits. Cook for about 2 minutes to allow the alcohol to evaporate. Add the chicken broth and simmer for another 5 minutes to reduce the sauce slightly.
Add the Chicken and Finish Cooking: Return the chicken breasts to the skillet, nestling them into the sauce. Reduce the heat to medium-low, cover the skillet, and let the chicken cook in the sauce for about 10 minutes or until cooked through and no longer pink in the center.
Thicken the Sauce: Uncover the skillet and remove the chicken breasts once again, placing them on a serving platter. Stir in the heavy cream into the sauce and continue cooking for an additional 2-3 minutes until the sauce thickens slightly.
Garnish and Serve: Pour the Marsala sauce over the chicken breasts on the serving platter. Sprinkle with fresh chopped parsley for a burst of freshness and color.