Cover chicken breast halves with a piece of plastic wrap and pound thin and flat with a meat mallet until chicken cutlets are about ¼” thick.
In a large pan, melt 1 tablespoon of butter and 2 tablespoons of olive oil over medium heat until nice and hot.
Meanwhile, mix together flour, salt, pepper, and dried oregano in a shallow dish.Dredge both sides of the chicken cutlets in the seasoned flour. Lightly coat and shake off excess.
Place the floured chicken cutlets in the hot pan and sear on both sides until golden brown. Remove cooked chicken from pan and set aside on a plate in a single layer.
In the same pan, melt 2 tablespoons of butter. Add onions and garlic to the pan and cook until onions are translucent and garlic is fragrant.
Wash and slice mushrooms, removing the stems. Add sliced mushrooms to the pan and saute until they are a deep brown color and moisture is gone.
Pour in marsala wine and chicken broth. Boil for a few minutes to reduce the sauce by half. Reduce heat and stir in the remaining tablespoon of butter.
Put chicken cutlets back into the pan and warm through on both sides.
Top with chopped parsley (optional)