01 - Butterfly each chicken breast and pound to 1/2-inch thickness between two sheets of plastic wrap. Season both sides generously with salt and pepper.
02 - Dredge each seasoned chicken cutlet in flour, pressing gently to adhere coating. Shake off excess flour and set aside.
03 - In a large skillet, heat 2 tbsp olive oil and 1 tbsp butter over medium-high heat until shimmering. Add chicken in batches, being careful not to overcrowd the pan. Cook for 3-4 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and tent loosely with foil.
04 - Add remaining 1 tbsp olive oil to the skillet. Pour in white wine, using a wooden spoon to scrape up browned bits from the bottom. Allow to simmer for 2 minutes until slightly reduced.
05 - Add chicken broth, lemon juice, and capers to the skillet. Simmer for 3-4 minutes, allowing the sauce to reduce slightly and intensify in flavor.
06 - Stir in remaining 1 tbsp butter until melted and incorporated. Return chicken to the pan and simmer for 2-3 minutes, spooning the sauce over the cutlets. Remove from heat, sprinkle with fresh parsley, and garnish with lemon slices. Serve immediately.