01 - Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Drain, reserving 1/2 cup of the pasta water.
02 - Slice chicken breasts in half horizontally to create thin cutlets. Season both sides with salt and pepper.
03 - Dredge chicken pieces in flour, shaking off excess.
04 - In a large skillet over medium-high heat, heat 2 tablespoons olive oil. Cook chicken in batches for 3–4 minutes per side, until golden and cooked through. Remove to a plate and cover loosely with foil.
05 - Add remaining 1 tablespoon olive oil and 2 tablespoons butter to same skillet. Add garlic and cook for 30 seconds until fragrant.
06 - Deglaze with white wine, scraping up browned bits. Simmer for 2 minutes.
07 - Stir in chicken broth, lemon juice, and capers. Simmer for 3–4 minutes until slightly reduced.
08 - Return chicken to skillet and simmer for 2 minutes, spooning sauce over the top.
09 - Add drained pasta, parsley, and Parmesan to the skillet. Toss everything together, adding reserved pasta water as needed for a silky sauce. Serve immediately, garnished with extra Parmesan and lemon slices if desired.