Slice chicken breasts in half horizontally to create thinner cutlets, or pound them to about 1/2-inch thick. In a shallow dish, combine flour, salt, and pepper. Dredge chicken cutlets in the flour mixture, shaking off excess.

Heat olive oil and butter in a large skillet over medium-high heat. Add chicken and cook for 3-4 minutes per side, until golden brown and cooked through. Remove chicken from skillet and set aside.

In the same skillet, add sliced mushrooms and cook for 5-7 minutes, stirring occasionally, until softened and browned. Add minced garlic and cook for another minute until fragrant.

Pour in the Marsala wine, scraping up any browned bits from the bottom of the skillet. Bring to a simmer and cook for 2-3 minutes until the wine has slightly reduced. Stir in the chicken broth.

Return the cooked chicken to the skillet, spooning the sauce over it. Simmer for 2-3 minutes to heat the chicken through and allow flavors to meld. Garnish with fresh parsley and serve immediately.