01 - Slice each chicken breast horizontally to create two thinner cutlets. Place between plastic wrap and gently pound to 1/2-inch thickness. Season both sides with salt and pepper.
02 - Lightly coat the chicken cutlets in flour, shaking off any excess.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Sear chicken for 3 to 4 minutes per side until golden and just cooked through. Transfer to a plate and cover loosely with foil to keep warm.
04 - Add dry white wine to the skillet, scraping up browned bits. Simmer for 1 to 2 minutes, then stir in chicken broth, lemon juice, and capers. Allow to simmer for 3 to 4 minutes to reduce slightly.
05 - Return chicken to the skillet and simmer in the sauce for 2 to 3 minutes, turning once to coat evenly. Remove from heat, then stir in the remaining 1 tablespoon butter and chopped parsley.
06 - Plate the chicken cutlets, spoon the sauce over the top, and garnish with lemon slices and additional parsley if desired. Serve immediately.