Place each chicken breast between two sheets of plastic wrap and gently pound to about 1/2 inch thickness. Slice into evenly sized cutlets. This ensures uniform cooking and juicy results.
In a shallow dish, combine the flour, salt, and black pepper. Dredge both sides of each chicken cutlet in the mixture, shaking off any excess. A light, even coating will help form a delicate crust.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. When shimmering, add the chicken and cook until golden brown and cooked through, about 2–3 minutes per side. Remove to a plate and tent with foil to keep warm.
In the same skillet, add the remaining tablespoon of olive oil. Add the mushrooms and sauté until they release their juices and become nicely browned, about 5–7 minutes. Stir in the garlic and cook for about 30 seconds until fragrant.
Pour in the Marsala wine to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer and reduce by half, about 3–5 minutes.
Add the chicken stock and simmer another 5 minutes, allowing the flavors to meld and the sauce to thicken slightly.
Stir in the butter until melted and glossy. Return the chicken to the skillet and simmer for 1–2 minutes to reheat and coat with the sauce. Finish with lemon juice and a pinch of salt if needed.
Remove from heat, garnish with chopped parsley, and serve immediately with your choice of side to soak up the sauce.