Take your boneless, skinless chicken breasts and place them between two layers of plastic wrap. Gently pound each breast to about ½-inch thickness using a meat tenderizer. This ensures they’ll cook evenly and retain a juicy texture.
Combine flour, lemon zest, salt, and pepper in a shallow bowl. Press each chicken breast into the mixture, coating both sides evenly. Shake off any excess before cooking.
Heat olive oil in a large skillet over medium-high heat. Sear each chicken breast for 4 to 5 minutes per side, until golden brown. Transfer to a plate and keep warm while you prepare the sauce.
Reduce the heat to medium and melt the butter in the same skillet. Stir in the flour and cook for about 2 minutes. Slowly pour in chicken broth while whisking to avoid lumps. Add the lemon juice, white wine (or extra broth), and capers. Simmer until slightly reduced.
Return the chicken breasts to the skillet, spooning the sauce over them. Simmer for another 2 to 3 minutes until the chicken is fully heated through and the sauce is thickened.
Sprinkle with fresh parsley and optional Parmesan cheese. Serve immediately over a bed of pasta, rice, or mashed potatoes.