01 - Place chicken breasts between two sheets of plastic wrap. Pound to an even 1/2-inch thickness for uniform cooking.
02 - Season both sides generously with salt and pepper. Dredge lightly in flour, shaking off excess to ensure light coating.
03 - In a large skillet over medium-high heat, combine olive oil and 2 tablespoons butter. Heat until sizzling and foam subsides.
04 - Add chicken to the hot pan. Sauté 3 to 4 minutes per side until golden brown and just cooked through. Transfer to a plate and tent with foil to keep warm.
05 - Pour white wine into the same skillet, scraping up browned bits from the bottom with a wooden spoon. Simmer 1 to 2 minutes until slightly reduced.
06 - Stir in chicken broth, lemon juice, and capers. Simmer 2 to 3 minutes until sauce thickens slightly and flavors meld.
07 - Return chicken to the skillet, spooning sauce over the top. Simmer 2 minutes until chicken is heated through.
08 - Remove from heat. Swirl in 1 tablespoon cold butter until melted and emulsified. Sprinkle with fresh parsley. Serve immediately, garnished with lemon slices and additional parsley if desired.