01 - Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Drain, reserving 1/2 cup of pasta water.
02 - Slice chicken breasts in half horizontally to create thin cutlets. Season both sides generously with salt and pepper.
03 - Lightly coat chicken pieces in flour, shaking off excess to ensure even coverage.
04 - Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Cook chicken in batches for 3–4 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil.
05 - Add remaining 1 tablespoon olive oil and 2 tablespoons butter to the same skillet. Sauté minced garlic for 30 seconds until fragrant.
06 - Pour in white wine, scraping up browned bits from the bottom of the skillet. Simmer for 2 minutes to reduce slightly.
07 - Stir in chicken broth, lemon juice, and capers. Simmer for 3–4 minutes until sauce begins to reduce and flavors meld.
08 - Return chicken to the skillet and simmer for 2 minutes, basting with the sauce to heat through.
09 - Add drained pasta, parsley, and Parmesan to the skillet. Toss vigorously to coat, adding reserved pasta water as needed for a silky consistency. Serve immediately with extra Parmesan and lemon slices if desired.