Begin by preparing the chicken; slice each chicken breast horizontally to create two thinner cutlets, then season both sides with salt and pepper. Dredge the seasoned chicken cutlets in flour, ensuring they are evenly coated, and set them aside on a plate.

Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once the pan is hot, add the flour-dredged chicken cutlets and cook for 3-5 minutes per side, or until golden brown and cooked through; remove the cooked chicken from the skillet and set aside.

In the same skillet, melt the remaining 1 tablespoon of butter, then add the sliced cremini mushrooms and cook until they are softened and lightly browned. Stir in the minced garlic and sauté for another minute until fragrant.

Pour in the Marsala wine and chicken broth, scraping the bottom of the pan to deglaze and incorporate all the flavorful browned bits. Bring the sauce to a simmer and cook for 5-7 minutes, or until it has slightly thickened.

Return the cooked chicken cutlets to the skillet, spooning the Marsala sauce over them to ensure they are well coated. Garnish with fresh chopped parsley and serve immediately with your preferred side dishes, such as pasta or mashed potatoes.