Place a chicken breast on a cutting board. Rest your one hand on the top of the chicken breast. Use a long sharp knife to slice the chicken breast in half so you have two thinner cutlets of chicken. Place a piece of plastic wrap over one chicken cutlet and pound it so that it is an even thickness. Flatten the other cutlet the same way. Do this with the remaining chicken breasts.
Sprinkle both sides of the chicken breast cutlets with salt and pepper.
Heat oil in a skillet over medium heat. Place the breaded chicken cutlets in the skillet and fry until cooked through, flipping hallway. Since these cutlets are thinner than a whole chicken breast, it will take less time to cook through, usually around 8-10 minutes. Depending on the size of the skillet, all the cutlets might not fit, so you may need to cook them in batches.
Remove the chicken cutlets from the skillet, for now, and place on a plate. Add the sliced mushrooms, minced shallots, marsala wine and chicken stock. Bring to a boil and cook for about 6-8 more minutes. The mushrooms and shallots should cook through and the liquid should reduce by about half.
Lower the heat to a medium low and stir in the cream. Place the chicken breast cutlets back into the skillet and flip them in the sauce so they are completely coated.
Continue to cook for 5 more minutes on low so the sauce thickens. Sprinkle with fresh parsley.