If not already thin, pound the chicken cutlets between plastic wrap to an even ¼-inch thickness. Season both sides with salt and pepper. Place flour in a shallow dish and dredge each piece of chicken, shaking off the excess.

In a large skillet over medium-high heat, add olive oil and 1 tbsp of butter. Once hot, add two chicken cutlets. Cook for 3-4 minutes per side until golden brown and cooked through. Remove to a plate and repeat with the remaining chicken.

Reduce heat to medium. Add another 1 tbsp of butter to the skillet. Add the sliced mushrooms and shallot. Cook for 5-7 minutes, until browned. Add the minced garlic and cook for 1 minute more until fragrant.

Pour in the dry Marsala wine, scraping up any browned bits from the bottom of the pan. Simmer until the wine has reduced by half, about 2-3 minutes. Add the chicken broth and simmer for 5-6 minutes, until the sauce begins to thicken.

Reduce heat to low and return the chicken to the skillet. Spoon the sauce over the chicken and let it warm through for 1-2 minutes. Turn off the heat. Stir in the remaining 1 tbsp of cold butter and the chopped parsley until the butter is melted and the sauce is glossy. Serve immediately.