Prep the chicken. If using whole breasts, slice them in half horizontally to make cutlets. Lightly pound to about 1/2-inch thickness. Pat dry and season both sides with salt and pepper.

Dredge in flour. Place flour on a plate. Lightly coat each cutlet, shaking off extra flour. This helps browning and gives the sauce body.

Brown the chicken. Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook the chicken in batches, 3–4 minutes per side, until golden and just cooked through. Transfer to a plate and tent with foil.

Cook the mushrooms. Add the remaining 1 tablespoon olive oil to the pan. Add mushrooms with a pinch of salt. Cook, stirring occasionally, until they release moisture and turn golden, about 6–8 minutes.

Add garlic and thyme. Stir in garlic and thyme for 30–45 seconds, just until fragrant. Avoid burning the garlic.

Deglaze with Marsala. Pour in the Marsala wine. Scrape up browned bits from the pan. Simmer 2–3 minutes to let the alcohol cook off and flavors deepen.

Add stock and reduce. Stir in chicken stock. Simmer 5–7 minutes until the sauce reduces by about one-third and slightly thickens.

Finish the sauce. Lower the heat. Whisk in 2 tablespoons cold butter. Add lemon juice if using. Taste and adjust salt and pepper.

Return chicken to the pan. Nestle the cutlets into the sauce and warm for 2 minutes. Spoon sauce over the top.

Garnish and serve. Sprinkle with parsley. Serve immediately over mashed potatoes, buttered noodles, or polenta.