Pound the chicken cutlets to a true 1/4\" thickness so they cook evenly in 3 to 4 minutes per side; uneven pieces will leave some parts overcooked and dry before others are done. The chicken is ready to flip when it releases easily from the pan and reads 165°F internal temperature.
Do not crowd the pan when searing the chicken; overcrowding steams instead of browns. Two batches in a large skillet give you a proper golden crust and maximize the fond that flavors the sauce.
The most common mistake is adding the Marsala wine before the mushrooms and onions are properly browned. Give the mushrooms a full 3 minutes undisturbed so they release and then reabsorb their moisture and develop deep color before deglazing.
For a richer, restaurant-style sauce, swap the Marsala cooking wine for dry Marsala wine. Cooking wine contains added salt and preservatives that can make the sauce taste flat; if you use it, taste before adding any extra salt.
The cooked chicken and sauce can be stored separately in airtight containers in the refrigerator for up to 3 days. Reheat gently in a covered skillet over low heat with a splash of chicken broth to loosen the sauce and prevent the chicken from drying out.