Start by slicing the chicken breasts in half horizontally. This creates four thinner pieces. Place them between sheets of plastic wrap. Use a mallet to pound them to an even thickness.

Sprinkle both sides of the chicken with salt and pepper. Put the flour in a shallow bowl. Dredge each piece of chicken in the flour. Shake off any extra flour before cooking.

Heat the oil and 2 tablespoons of butter in a large skillet. Wait until the pan is nice and hot. Add the chicken pieces. Cook for 3 minutes on each side until golden brown.

Once the chicken is cooked through, take it out of the skillet. Place the pieces on a clean plate. Tent them loosely with foil to keep them warm. Do not clean the pan yet!

Add the lemon juice, chicken stock, and capers to the same skillet. Use a whisk to scrape up the brown bits. These bits hold all the flavor. Bring the liquid to a simmer.

Let the sauce reduce for a few minutes. Add the remaining 2 tablespoons of butter. Whisk it in until the sauce looks glossy. This makes the sauce rich and smooth.

Put the chicken back into the skillet for one minute. Spoon the warm sauce over the meat. Sprinkle with fresh parsley. Serve immediately while the chicken is still crispy.