01 - Slice each chicken breast horizontally to create 4 thin cutlets. Pat dry thoroughly with paper towels and season both sides generously with salt and pepper.
02 - Lightly coat each cutlet in flour, shaking off any excess. Set aside on a clean plate.
03 - Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat. Once shimmering, add chicken cutlets in a single layer without crowding. Cook 2 to 3 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil.
04 - Pour wine into the hot skillet, using a wooden spoon to scrape up any browned bits from the bottom. Simmer for 2 minutes to reduce slightly.
05 - Add chicken broth, lemon juice, and capers to the skillet. Simmer for 3 to 4 minutes until the sauce reduces and thickens slightly.
06 - Reduce heat to low. Swirl in remaining 2 tablespoons butter until melted and the sauce becomes glossy and emulsified.
07 - Return chicken cutlets and any accumulated juices to the skillet. Simmer for 1 to 2 minutes until heated through. Transfer to serving plates, spoon sauce generously over the chicken, and garnish with fresh parsley.