01 - Place chicken breasts between two pieces of plastic wrap and gently pound to an even 1/2-inch thickness. Season both sides with salt and pepper.
02 - Dredge each chicken breast in flour, shaking off excess.
03 - In a large skillet, heat 2 tablespoons olive oil and 1 tablespoon butter over medium-high heat. Add chicken breasts and cook for 4–5 minutes per side, until golden and cooked through. Remove chicken to a plate and cover loosely with foil.
04 - Add remaining 1 tablespoon olive oil and 1 tablespoon butter to the skillet. Add sliced mushrooms and sauté for 5–6 minutes, stirring occasionally, until browned and tender.
05 - Add minced garlic and thyme; cook for 30 seconds until fragrant.
06 - Pour in Marsala wine, scraping up any browned bits from the bottom of the pan. Simmer for 2–3 minutes to reduce slightly.
07 - Add chicken broth and bring to a gentle simmer. Cook for 3–4 minutes until sauce thickens slightly. Stir in heavy cream if using.
08 - Return chicken (and any accumulated juices) to the skillet. Simmer for 2–3 minutes, spooning sauce over the chicken until heated through. Remove from heat. Sprinkle with chopped parsley and serve immediately, optionally with lemon wedges.