Prepare the Chicken: Place the chicken breasts between two pieces of plastic wrap and pound them to an even thickness of about 1/4 inch. Season both sides generously with 1/2 tsp salt and 1/4 tsp pepper.

Dredge the Chicken: In a shallow dish, combine the flour with the remaining 1/2 tsp salt and 1/4 tsp pepper. Lightly coat each chicken cutlet in the flour mixture, shaking off any excess.

Sear the Chicken: Heat olive oil and 2 tbsp of butter in a large skillet over medium-high heat. Place the chicken in the skillet in a single layer (work in batches if needed). Cook for 3-4 minutes per side, until golden brown and cooked through. Remove the chicken and set it aside.

Sauté the Aromatics: In the same skillet, melt the remaining 2 tbsp of butter. Add the sliced mushrooms and cook until they have released their moisture and started to brown, about 5-7 minutes. Add the minced shallot and garlic and cook for another minute until fragrant.

Deglaze and Build the Sauce: Pour in the Marsala wine to deglaze the pan, scraping up any browned bits from the bottom. Allow the wine to simmer and reduce by about half, which should take 2-3 minutes.

Simmer: Stir in the chicken broth and bring the sauce to a simmer. Let it cook for 5-8 minutes, allowing the sauce to thicken slightly. If using, stir in the heavy cream.

Combine and Serve: Return the cooked chicken to the skillet, spooning the sauce over the top. Let it simmer for another minute to heat through. Garnish with fresh parsley and serve immediately.