Prepare Chicken - Place one of the chicken pieces between two plastic sheets or in a large plastic bag. Use a meat tenderizer to flatten to an even thickness, about ½-inch thick. Repeat with the remaining pieces.Alternatively, for pieces larger than 1 inch thick and heavier than 8 ounces, cut in half horizontally. This should create eight ½-inch thick pieces.
Season Chicken - Lightly season each side of the chicken breast with salt and pepper.
Coat Chicken - In a medium bowl, combine flour, 1 teaspoon salt, and 1/2 teaspoon pepper. Dredge the pieces in the seasoned flour, shaking off any excess. Transfer to a plate and set aside.
Cook Chicken - Heat a large skillet over medium-high heat. Add the olive oil. Once hot, carefully add the chicken to the pan. Cook until golden brown, about 4 to 6 minutes.Reduce the heat to medium. Flip the pieces and cook until the internal temperature reaches 160 to 165ºF (71 to 74ºC) on a meat thermometer, about 4 to 6 minutes. Fry in batches if needed. Transfer to a clean plate, and loosely tent with foil to keep warm. Reserve the pan to saute the mushrooms.
Saute the Mushrooms - Melt the butter over medium heat. Add the onions and garlic, and sauté for 1 minute, stirring to ensure the garlic does not brown.Add the mushrooms, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Sauté until tender, about 5 minutes.
Make the Sauce - Turn the heat up to medium-high and add the Marsala wine. Cook until reduced by half, about 2 minutes. Add the chicken stock. Cook until the sauce is reduced by 1/2 (about 1/2 cup), about 5 to 7 minutes.Reduce the heat to medium, and stir in the cream. Simmer until the sauce has thickened, about 3 to 5 minutes—season to taste with salt and pepper.
To Serve - Add the chicken back to the pan, turn to coat, and gently simmer until warmed through, about 1 to 2 minutes. Garnish with chopped parsley and serve hot.
Notes
Storing: Cool completely, then transfer to an airtight container and refrigerate for up to 5 days.
Reheating: Cover and reheat on high setting in the microwave in 15 to 30-second increments until hot.
Marsala wine substitute: Madeira, port, grape juice plus 2 teaspoons of brandy, riesling, or Moscato d'asti. Non-alcoholic options are red grape juice, adding an additional ½ cup of chicken stock plus 1 tablespoon of balsamic vinegar, and 1 ½ teaspoon of sugar.
Heavy cream substitute: Omit heavy cream and whisk in 3 tablespoons cold butter to thicken the sauce over low heat. Add chicken to warm for a few minutes.