01 - Butterfly each chicken breast by slicing horizontally through the center, then gently pound to ½-inch thickness between plastic wrap. Season both sides generously with salt and pepper.
02 - Lightly coat each chicken breast in flour, shaking off any excess to ensure an even, thin layer.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken and cook for 3–4 minutes per side until golden brown and cooked through. Transfer to a plate and tent loosely with foil to keep warm.
04 - Pour white wine into the hot skillet, scraping up any browned bits from the bottom with a wooden spoon. Simmer for 1–2 minutes until slightly reduced.
05 - Add chicken broth, lemon juice, and capers to the pan. Simmer for 2–3 minutes, allowing the sauce to reduce by about one-third and intensify in flavor.
06 - Return chicken to the skillet and simmer for 2 minutes, spooning the sauce over the meat. Remove from heat and stir in the remaining 1 tablespoon butter and half the parsley until the sauce becomes glossy and emulsified.
07 - Transfer chicken to serving plates. Spoon remaining sauce over the top and garnish with fresh lemon slices and the reserved parsley.