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