01 - Place chicken cutlets between two sheets of plastic wrap and gently pound to an even 1/2-inch thickness.
02 - In a shallow dish, combine flour, salt, and pepper. Dredge each cutlet in the mixture, shaking off excess.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add cutlets and cook 2–3 minutes per side until golden and cooked through. Work in batches if necessary. Remove chicken and keep warm.
04 - Reduce heat to medium. Pour in white wine and scrape browned bits from skillet. Simmer 1–2 minutes until reduced by half.
05 - Add chicken broth, lemon juice, and capers to skillet. Simmer 2–3 minutes allowing sauce to thicken slightly.
06 - Return chicken cutlets to skillet, spoon sauce over them, and cook 1–2 minutes until heated through.
07 - Stir in remaining 1 tablespoon butter for a silky finish, if desired.
08 - Sprinkle chopped parsley over chicken and serve immediately.