Slice the chicken breasts in half horizontally to create four thinner cutlets. Season both sides evenly with salt and black pepper.
Place the flour in a shallow dish. Dredge each chicken cutlet in the flour, shaking off any excess.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken cutlets and pan-fry for 4 to 5 minutes per side until golden brown and cooked through. Transfer the chicken to a plate and cover loosely to keep warm.
In the same skillet, melt another tablespoon of butter. Add the sliced mushrooms and cook for 5 to 6 minutes until browned and softened.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the Marsala wine and chicken stock, scraping up any browned bits from the bottom of the pan. Simmer for 5 minutes until the liquid is reduced by half.
Stir in the heavy cream and the remaining tablespoon of butter. Let the sauce simmer for 2 to 3 minutes until thickened.
Return the chicken cutlets to the skillet, spooning the creamy mushroom sauce over them. Simmer for 2 minutes to heat the chicken through.
Garnish with chopped fresh parsley and serve immediately.