Pound the chicken even: Place each chicken breast between sheets of plastic wrap and pound to an even 1/2-inch thickness. This helps the chicken cook evenly and quickly in the skillet.

Season and dredge: Mix the flour with salt and pepper on a plate. Dredge each piece of chicken in the flour, shaking off the excess so only a thin coating remains.

Heat the skillet: Heat the olive oil and 2 tablespoons of butter in a large skillet over medium-high heat until the butter foams. The pan should be hot enough that the chicken sizzles right away.

Sear the chicken: Add the chicken and cook for about 4 minutes per side, until the crust turns deep golden and the internal temperature reaches 165°F. Transfer the chicken to a plate and tent loosely with foil.

Cook the garlic: Lower the heat to medium and add the remaining 2 tablespoons of butter to the same skillet. Stir in the garlic and cook for about 30 seconds, until fragrant but not browned.

Deglaze the pan: Pour in the chicken broth and scrape up the browned bits stuck to the bottom of the skillet with a wooden spoon. These bits add flavor and color to the sauce.

Add lemon juice and zest: Whisk in the lemon juice and zest, then bring the sauce to a gentle simmer. Let it cook for 3 to 4 minutes, until it reduces slightly and coats the back of a spoon.

Return chicken to sauce: Nestle the chicken back into the skillet along with any juices from the plate. Spoon the sauce over the top and simmer for 2 minutes to warm the chicken through.

Finish and serve: Sprinkle the chopped parsley over the chicken before bringing the skillet to the table. Spoon extra sauce over each piece when plating.