Place chicken breasts between plastic wrap or parchment paper and pound to ½ inch thickness using a meat mallet or rolling pin. Pat completely dry with paper towels. Season both sides with salt and pepper. Dredge in all-purpose flour, shaking off excess flour to ensure a light coating.
4 pieces chicken breast, 0.5 cup all-purpose flour, to taste salt and black pepper
Heat olive oil in a large heavy skillet over medium-high heat for 3-4 minutes until shimmering. Add chicken breasts without crowding the pan and cook 4-5 minutes per side until golden brown and internal temperature reaches 165°F. Transfer cooked chicken to a plate and tent with foil.
4 pieces chicken breast, 2 tablespoons olive oil
Add 1 tablespoon butter to the same skillet over medium-high heat. Add sliced mushrooms in a single layer and cook without stirring for 4-5 minutes until golden brown on one side. Stir and cook for an additional 2 minutes. Add minced garlic and cook for 30 seconds until fragrant.
3 tablespoons butter, 8 ounces cremini mushrooms, 2 cloves garlic
Remove the skillet from heat and pour in the sweet Marsala wine, scraping up browned bits from the bottom with a wooden spoon. Return pan to medium heat, add chicken broth, and simmer for 5-7 minutes until sauce is reduced by about half and coats the back of a spoon. Stir in remaining 2 tablespoons butter until melted and glossy.
0.75 cup sweet Marsala wine, 0.75 cup chicken broth, 3 tablespoons butter
Return the chicken breasts to the skillet and spoon sauce over the top. Simmer for 1-2 minutes to reheat the chicken. Taste and adjust salt if needed. Garnish with fresh chopped parsley and serve immediately.
4 pieces chicken breast, for garnish fresh parsley, to taste salt and black pepper