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 chicken broth, wine and lemon juice. Cook, stirring occasionally, until slightly reduced, about 5 minutes.
Gradually whisk in heavy cream until slightly thickened, about 3-4 minutes; season with salt and pepper, to taste. Stir in capers.
Serve immediately with pasta and chicken, garnished with parsley, if desired.
Notes
*Additional chicken broth can be used for white wine as a non-alcoholic substitute.