01 - Butterfly each chicken breast by slicing horizontally through the center. Gently pound to 1/2-inch thickness between plastic wrap. Season both sides generously with salt and black pepper.
02 - Lightly coat each chicken breast in flour, shaking off any excess. Ensure an even, thin coating for proper browning.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken and cook 3-4 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil to keep warm.
04 - Pour white wine into the hot skillet, scraping up any browned bits from the bottom. 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 approximately one-third and thicken slightly.
06 - Return chicken to the skillet and simmer for 2 minutes, spooning sauce over the meat. Remove from heat and stir in remaining 1 tablespoon butter and half the parsley until sauce is glossy and emulsified.
07 - Transfer chicken to serving plates. Spoon remaining sauce generously over each piece. Garnish with lemon slices and remaining fresh parsley.