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