Slice the chicken breasts in half horizontally to create four thin cutlets. Place them between two sheets of plastic wrap. Use a meat mallet to pound them to an even thickness.

Mix the flour, salt, and pepper in a shallow dish. Dip each chicken piece into the flour mixture. Shake off any extra flour so only a thin coating remains on the meat.

Place a large skillet over medium-high heat. Add the olive oil and one tablespoon of butter. Wait until the butter melts and starts to shimmer before adding the chicken to the pan.

Place the chicken cutlets in the hot pan. Cook for about three minutes per side until golden brown. Once cooked through, move the chicken to a warm plate and cover it loosely.

Pour the chicken stock or white wine into the hot skillet. Use a wooden spoon to scrape up the brown bits from the bottom. These bits hold all the best flavor.

Stir in the fresh lemon juice and the drained capers. Let the liquid simmer for about two minutes. The sauce should reduce slightly and become a bit thicker as it bubbles.

Turn the heat down to low. Whisk in the remaining two tablespoons of butter until the sauce is smooth and glossy. This creates a rich texture that coats the chicken beautifully.

Place the cooked chicken back into the skillet for one minute. Spoon the sauce over the meat. Sprinkle with fresh parsley and add lemon slices before serving your delicious meal.