In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
Season chicken with salt and pepper, to taste. Working one at a time, dredge chicken in flour.
Melt 2 tablespoons butter in a large cast iron skillet over medium high heat. Add chicken and cook, flipping once, until cooked through, about 4-5 minutes on each side. Set aside and keep warm.
Melt remaining 2 tablespoons butter in the skillet. Add garlic and shallots, and cook, stirring frequently, until fragrant, about 2 minutes.
Stir in wine, scraping any browned bits from the bottom of the skillet.
Stir in chicken broth and lemon juice. Cook, stirring occasionally, until slightly reduced, about 5 minutes.
Reduce heat to low; gradually stir in heavy cream until slightly thickened, about 3-4 minutes.
Stir in capers; season with salt and pepper, to taste. Return chicken to the skillet.
Serve immediately with pasta, garnished with parsley, if desired.
Notes
Cut the chicken lengthwise. Rather than pounding out the chicken, cut the chicken breasts lengthwise, slicing horizontally across the thickest part of the breasts – this will create uniform cutlets and allow fast cooking so the meat stays tender without drying out.
Avoid an overcrowded pan. Cook the chicken cutlets in batches to ensure proper browning for a golden brown crust. An overcrowded pan will steam the chicken instead!
Deglaze the pan. This will help build the pan sauce by adding all the deep, concentrated flavors from the caramelized browned bits stuck to the bottom of the pan.
Choose a wine you will drink. A dry white wine (pinot grigio or sauvignon blanc) is great here – it does not have to be anything fancy or overpriced. Just something you don’t mind sipping on since you will have an open bottle.
Add the cream slowly. Always add the heavy cream at the very end, pouring very slowly to prevent curdling.
Serve over a bed of pasta. The pasta will soak up all the extra sauce, transforming a simple chicken dish into a hearty dinner without requiring heavy sides.
Mix it up. Swap out the chicken for veal or shrimp.