It is easiest to pound the chicken between two sheets of plastic wrap, or in a study zip-top freezer bag. Spritz the chicken with a little water to prevent the meat from tearing. Season the breasts with salt and pepper and dredge in the flour. Shake off the excess flour -- add more flour if needed.
In a 12" skillet heat 2 tbsp. olive oil and 1 tbsp. butter over medium-high heat. Add the chicken to the pan but don't crowd then. Cook chicken breasts, turning them over midway during cooking, until they are browned on each side. They don't have to be completely cooked through at this point. When browned, transfer the chicken to a large platter and set aside.
Add 2 tbsp. olive oil and 1 tablespoon butter to the skillet over high heat until the butter starts to sizzle. Add the sliced mushrooms, season with salt and pepper, and cook, stirring occasionally, until the mushrooms are a golden brown, about 8-10 minutes. Transfer the mushrooms to the platter with the chicken.
Heat remaining 1 tablespoon olive oil in the skillet, add shallots and garlic; sauté, stirring, until soft, about 1-2 minutes. Stir the cornstarch into the chicken stock until it is completely dissolved, then mix it with the Marsala. Add the liquid to the skillet; cook, stirring and scraping bottom of pan until slightly thickened, about 2 minutes. Add the mushrooms and the chicken to the skillet and cook the the sauce over medium heat, turning the chicken over occasionally, to make sure the breasts are well-basted about 4 - 5 minutes. Remove from heat; stir in remaining 3 Tablespoons butter and chopped parsley. Taste the sauce to make sure it is well seasoned with salt and pepper. Enjoy the rich flavor in the chicken and sauce served with your choice of pasta or egg noodles.