Prepare Chicken: Pat chicken breasts dry. In a shallow dish, combine flour, salt, and pepper. Dredge each chicken cutlet in the flour mixture, shaking off any excess. Set aside.
Sear Chicken: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add chicken cutlets in a single layer (work in batches if necessary to avoid overcrowding). Sear for 3-4 minutes per side, or until golden brown and cooked through. Remove chicken from skillet and set aside on a plate.
Sauté Mushrooms & Aromatics: Reduce heat to medium. Add butter to the same skillet. Add sliced mushrooms and cook for 5-7 minutes, stirring occasionally, until softened and browned. Add shallots and garlic, cooking for another 2-3 minutes until fragrant. Scrape up any browned bits from the bottom of the pan.
Deglaze with Marsala: Pour in the Marsala wine, scraping the bottom of the pan with a wooden spoon to deglaze and release all the flavorful fond. Bring to a simmer and cook for 3-5 minutes, allowing the wine to reduce by about half. The alcohol will cook off, leaving a rich, concentrated flavor.
Simmer Sauce: Stir in the chicken broth and bring to a gentle simmer. Cook for 5 minutes until the sauce begins to thicken slightly. Reduce heat to low, then slowly stir in the heavy cream. Continue to simmer gently for 2-3 minutes, allowing the sauce to meld and thicken further. Do not boil once cream is added.
Combine and Serve: Return the seared chicken cutlets to the skillet, spooning the creamy Marsala sauce over them. Heat through for 1-2 minutes until chicken is warm. Garnish with fresh chopped parsley and serve immediately.