After butterflying the chicken into four pieces, cover with plastic wrap and gently pound with a meat mallet to flatten and tenderize.
Season cutlets with salt and pepper, then dredge evenly in flour, shaking off excess.
Heat oil and 1 tablespoon butter in a large skillet over medium-high heat.
Fry chicken for 3 minutes per side until golden brown, then remove to a plate.
Pour broth, wine, lemon juice, and capers into the hot skillet, scraping up any browned bits.
Add lemon slices and bring to a boil and let the liquid reduce by half, approximately 3 minutes.
Whisk in the remaining 2 tablespoons of butter, return chicken to pan, and garnish with parsley.
Meanwhile, boil a large pot of heavily salted water (about 1 tablespoon of salt) and 1 tablespoon of oil.
Cook the pasta for 3-5 minutes and then drain.
Serve the chicken over the pasta.