Prepare the Chicken Cutlets: Begin by slicing the chicken breasts horizontally to create four even cutlets. Place them between two sheets of plastic wrap or inside a zip-top bag and gently pound with a meat mallet or rolling pin until they are about one-third of an inch thick. Season both sides evenly with salt and pepper. Next, lightly coat each piece with flour, shaking off any excess to prevent clumping.
Brown the Chicken: Heat a large, heavy-bottomed skillet over medium heat. Add the olive oil and butter, letting the butter melt and combine with the oil. When the mixture is hot and shimmering, add the floured chicken cutlets. Cook for 3 to 4 minutes on each side, or until they develop a golden-brown crust and reach an internal temperature of 165°F. Transfer the chicken to a plate and tent with foil to keep warm.
Sauté the Mushrooms and Aromatics: If needed, add a splash of olive oil to the same pan. Toss in the mushrooms and sauté until their moisture evaporates and they turn golden brown, about 5 minutes. Sprinkle the onion powder over the mushrooms, then stir in the minced garlic. Cook for another 30 seconds, stirring constantly until fragrant.
Deglaze and Simmer the Sauce: Pour in the Marsala wine, scraping the bottom of the pan to release any browned bits (fond) left from the chicken. Turn up the heat and let the wine reduce by about half, which should take 4 to 5 minutes. Next, add the chicken broth and gradually stream in the heavy cream while stirring to combine. Lower the heat and let the sauce simmer gently for another 4 to 5 minutes until it thickens slightly. Taste and adjust seasoning with salt if needed.
Finish the Dish: Return the cooked chicken to the pan, nestling it into the sauce. Sprinkle with fresh parsley and spoon sauce generously over each piece. Warm everything together on low heat for 2 minutes to meld flavors and thicken the sauce to your preferred consistency. Remember, the sauce will continue to thicken as it cools.
