01 - Place chicken breasts between two sheets of plastic wrap and gently pound to 1/2-inch thickness. Season both sides with salt and pepper, then dredge in flour, shaking off excess.
02 - Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add chicken and cook 3-4 minutes per side until golden brown and just cooked through. Transfer to a plate and tent with foil.
03 - Add remaining 1 tablespoon olive oil and the butter to the skillet. Add mushrooms and cook 5-6 minutes, stirring occasionally, until browned and their liquid has evaporated.
04 - Add garlic and sauté for 30 seconds until fragrant.
05 - Pour in Marsala wine, scraping up any browned bits. Simmer 2-3 minutes to reduce slightly.
06 - Add chicken broth and return chicken breasts (and any juices) to the skillet. Simmer 7-8 minutes, turning chicken once, until sauce has thickened slightly.
07 - Stir in heavy cream if using, and simmer for 1 minute.
08 - Remove from heat. Sprinkle with chopped parsley and serve immediately, with lemon wedges if desired.