Place chicken halves between two sheets of plastic wrap. Use a meat mallet to pound them until thin. Aim for about 1/4-inch thickness. This ensures the chicken cooks fast and stays juicy.

Sprinkle both sides of the chicken with salt and pepper. Place the flour in a shallow dish. Dredge each piece of chicken in the flour. Shake off the extra flour so it is lightly coated.

Heat the oil and 1 tablespoon of butter in a large skillet. Use medium-high heat. Place the chicken in the pan. Cook for about 3 minutes per side. It should be golden brown and cooked through.

Take the chicken out of the skillet. Place it on a clean plate or a warm platter. Cover it loosely with foil to keep it warm. Do not clean the pan yet! Those browned bits are pure flavor.

Add the white wine to the hot skillet. Use a wooden spoon to scrape the bottom of the pan. Let the wine simmer until it reduces by half. This removes the alcohol bite and leaves great taste.

Stir in the chicken stock, lemon juice, and capers. Bring the liquid to a simmer. Let it cook for about 3 to 5 minutes. The sauce should thicken slightly as it bubbles away in the pan.

Turn the heat to low. Add the remaining 3 tablespoons of cold butter. Whisk it into the sauce until it is creamy and smooth. This creates that famous, velvety texture Martha Stewart loves.

Place the chicken back into the skillet for one minute. Spoon the warm lemon sauce over the top. Garnish with plenty of fresh parsley. Serve immediately while the sauce is hot and glossy.