Prepare the chicken: Place each chicken cutlet between sheets of plastic wrap and gently pound to about 1/4 inch thickness. This helps them cook quickly and evenly.
Set up a breading station: Place flour in a shallow dish. In another dish, beat the eggs. Lightly season both sides of the chicken with salt and pepper.
Dredge the chicken in flour, tapping off any excess. Dip into the beaten eggs, letting excess drip off.
Sear the chicken: In a large skillet, heat olive oil over medium-high heat. Add the chicken and cook 2–3 minutes per side, until golden brown. Remove to a plate and cover loosely to keep warm.
Make the mushroom base: In the same skillet, add butter. Once melted, add mushrooms and cook until they release their moisture and start to brown, about 5–7 minutes. Stir in minced garlic and cook for another 30 seconds.
Deglaze and flavor: Pour in Marsala wine to deglaze, scraping up any browned bits from the bottom of the pan. Simmer until reduced by about half, 3–4 minutes.
Finish the sauce: Add chicken stock and bring to a simmer. Return the chicken to the pan and cook for 4–6 minutes, until the chicken is cooked through and the sauce thickens slightly.
Finish with brightness: Stir in lemon juice (if using) and chopped parsley. Season to taste with salt and pepper.
Serve: Spoon the sauce and mushrooms over the chicken. Pair with mashed potatoes, pasta, or crusty bread to soak up the sauce.