Pat the chicken dry and slice or pound thick breasts to an even thickness.
Season both sides with salt and black pepper.
Lightly coat each piece in flour and shake off excess.
Heat olive oil in a skillet and sear chicken 3–4 minutes per side until golden and cooked through, then transfer to a plate.
Cook sliced mushrooms 4–5 minutes until tender and browned.
Add minced garlic and cook 30 seconds.
Add Marsala wine, scrape browned bits, and simmer 2–3 minutes.
Add chicken broth and simmer 3–5 minutes until the sauce starts to thicken.
Lower heat and stir in butter and heavy cream without boiling hard.
Return chicken and simmer gently for about 2 minutes.
Taste and adjust seasoning.
Garnish with parsley and serve with the mushroom sauce.