Place the flour, salt and pepper in a resealable plastic bag, shaking to combine, and set aside. Alternately, you can combine the ingredients in a shallow dish, such as a pie pan.
Place one chicken breast on a cutting board and cover with plastic wrap. Using a meat mallet or rolling pin, pound the chicken breast until it’s 1/4-inch thickness. Repeat with the remaining breasts. (Note: if the chicken breasts are on the larger size, you can butterfly them prior to flattening, which will double the recipe yield. See notes).
Place the flattened chicken in the bag with the flour mixture. Seal and shake to combine. (If you’re using a shallow dish, use tongs to dip each breast into the flour mixture, tapping off the excess.
Heat 1 tablespoon olive oil in a 12-inch skillet set over medium-high heat. Once the oil is shimmering and thin, add 1 tablespoon butter and swirl the pan around. Add 2 chicken breasts and pan sear until golden brown on both sides, approximately 3-4 minutes per side. Remove the chicken from the pan and set on a clean dish or cutting board and set aside. Cover with aluminum foil to keep warm. Repeat with the remaining chicken, adding the remaining oil and butter first if needed.
Once the chicken is cooked and set aside, adjust the heat to medium-low. Add the pancetta and cook, stirring with a spatula, until crispy and brown, 3-4 minutes. Scrape up any brown bits on the bottom of the pan left from the chicken and stir them in with the pancetta. Add the shallots and continue cooking for an additional minute while stirring, then add the mushrooms. Cook, stirring frequently, until the mushrooms have softened, darkened, and decreased in size, around 3 minutes. Add the garlic and cook for an additional minute.
Pour the marsala wine into the pan, using a spatula to scrape up any brown bits that are stuck to the bottom. Add the stock and bring the liquids to a simmer. Cook until the sauce has reduced by half, 12-15 minutes.
Stir in the cream and add the chicken back to the pan, stirring to coat. Cook for an additional 3-5 minutes, or until the sauce thickens and the chicken is warmed through.
Before serving, top with the chopped parsley. Store any leftovers in an airtight container in the refrigerator for up to four days.
How to butterfly a chicken breast (optional step):
Set the chicken breast on a cutting board and place your hand firmly on top.
Keeping your fingers lifted out of the way, use a sharp chef’s knife to slice the breast in half lengthwise, starting with the thicker end. Avoid slicing motions by starting with the back end of the blade and pulling it toward you. Then lift the breast open and continue slicing through the center in single strokes until you cut through to the other side. Slice in half.
Optionally, you can further thin out the halves by placing plastic wrap over each one and then pounding with a meat mallet or rolling pin.