Slice each chicken breast in half horizontally to make thin cutlets. Place them between two sheets of parchment and pound to an even 0.5 inch thickness. Season both sides with the salt and pepper.

Put the flour on a plate. Dredge each cutlet lightly and shake off the excess so only a thin dusting remains.

Heat the olive oil in a large skillet over medium high until it shimmers. Add the cutlets in a single layer, working in two batches if needed, and cook 3 minutes per side until golden and 165°F inside. Transfer to a plate.

Lower the heat to medium. Add the minced garlic and stir for 30 seconds until fragrant.

Pour in the broth, lemon juice, and lemon zest, scraping up the browned bits from the bottom of the pan. Rinse the capers, add them, and simmer 3 to 4 minutes until the sauce reduces by about a third.

Turn off the heat. Add the butter and swirl the pan until it melts into the sauce and turns glossy.

Return the chicken and any juices to the skillet and spoon the sauce over the cutlets for about 1 minute to warm through.

Scatter with parsley and serve right away with extra lemon wedges if you like.