In a shallow dish, combine flour, salt, and black pepper.
Dredge chicken cutlets in the flour mixture, shaking off any excess.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Sear chicken for 3 to 4 minutes per side until golden brown and cooked through. Remove chicken from skillet and set aside.
Add the remaining 2 tablespoons of butter to the same skillet. Add mushrooms and sauté for 5 to 7 minutes until browned and moisture has evaporated.
Add minced garlic and cook for 1 minute until fragrant.
Pour in the Marsala wine to deglaze the pan, scraping the bottom to release the fond. Simmer until liquid is reduced by half.
Stir in the chicken broth and heavy cream. Bring to a gentle simmer.
Return the chicken to the skillet. Simmer for 3 to 5 minutes until the sauce thickens to a coating consistency.
Garnish with chopped parsley and serve immediately.