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 to ensure light coating.
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.
09 - Remove from heat. Sprinkle with chopped parsley and serve immediately, optionally with lemon wedges.