01 - Slice each chicken breast horizontally to create 4 thin cutlets. Pat cutlets completely dry with paper towels, then season both sides generously with salt and freshly ground black pepper.
02 - Lightly dredge each cutlet in flour, coating both sides evenly. Shake off any excess flour to prevent a heavy coating.
03 - Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat until butter foams. Add chicken in a single layer, cooking in batches if necessary to avoid overcrowding. Sauté for 2-3 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil to rest.
04 - Pour wine into the hot skillet, using a wooden spoon to scrape up any browned bits from the bottom. Let the wine simmer for 2 minutes to reduce slightly.
05 - Add chicken broth, lemon juice, and capers to the skillet. Simmer for 3-4 minutes until the liquid reduces by about one-third.
06 - Reduce heat to low. Add remaining 2 tablespoons butter, swirling the pan constantly until the butter melts and the sauce becomes glossy and emulsified.
07 - Return chicken cutlets and any accumulated juices to the skillet. Simmer for 1-2 minutes until heated through. Plate the chicken, spoon sauce generously over each cutlet, and garnish with chopped fresh parsley.